SquareWell_oskireeva.ipynb

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        "Before you turn this problem in, make sure everything runs as expected. First, **restart the kernel** (in the menubar, select Kernel$\\rightarrow$Restart) and then **run all cells** (in the menubar, select Cell$\\rightarrow$Run All).\n",
        "\n",
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      "source": [
        "---"
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      "source": [
        "import numpy as np\n",
        "import matplotlib.pyplot as plt"
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        "# 1D square well\n",
        "\n",
        "Consider a quantum particle, described by the wave function $\\psi(x)$ moving in an external potential $V(x)$.\n",
        "For simplicity, only consider a one-dimensional real variable $x$.\n",
        "\n",
        "The wave function of a particle obeys the Schoedinger equation\n",
        "\n",
        "\n",
        "$$\n",
        "-\\frac{\\hbar^2}{2m} \\psi''(x)  + V(x)\\psi(x) = E\\psi(x)\\;.\n",
        "$$\n",
        "\n",
        "Here $\\hbar$ is the Planck's constant, $m$ is the mass of the particle (both are known), and $E$ is the energy of the particle.\n",
        "\n",
        "Given boundary conditions, the non-zero solution for $\\psi(x)$ _only exists for some values of the energies_. Physisists say that the energy of a particle is _quantized_. Mathematicians say that the problem is nothing but the eigenvalue problem of the Sturm-Liouville operator\n",
        "\n",
        "\n",
        "$$\n",
        "L = -\\frac{\\hbar^2}{2m}\\frac{d^2}{dx^2} + V(x) \\;.\n",
        "$$\n",
        "\n",
        "\n",
        "Here we consider the so-called square well potential, \n",
        "\n",
        "$$\n",
        "V(x) = %\n",
        "\\begin{cases}\n",
        "&0, &0 < x < a \\\\\n",
        "&\\infty, &\\text{otherwise.} \n",
        "\\end{cases}\n",
        "$$\n",
        "\n",
        "Define\n",
        "$$\n",
        "E = \\frac{\\hbar^2}{2m} k^2\n",
        "$$\n",
        "\n",
        "The Schroedinger equation for $0 < x < a$ becomes\n",
        "\n",
        "$$\n",
        "\\psi''(x) = -k^2 \\psi(x)\n",
        "$$\n",
        "\n",
        "with the boundary conditions $\\psi(0) = \\psi(a) = 0$.\n",
        "\n",
        "Solutions are\n",
        "\n",
        "$$\\psi_n(x) = \\sqrt{\\frac{2}{a}} \\sin{k_n x}$$\n",
        "\n",
        "\n",
        "with\n",
        "\n",
        "$$\n",
        "k_n a = \\pi n\\;, \\qquad n = 1, 2, \\cdots\n",
        "$$\n",
        "\n",
        "So that the eigenenergies are\n",
        "\n",
        "$$\n",
        "E_n = \\frac{\\pi^2\\hbar^2}{2ma^2} n^2\n",
        "$$"
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        "## Eigenfunctions, numerically\n",
        "\n",
        "Define a mesh\n",
        "\n",
        "$$x_j = a \\frac{j}{N}, \\qquad j=0, \\cdots, N\n",
        "$$\n",
        "\n",
        "and the mesh function $\\psi_j$.\n",
        "\n",
        "The Schroedinger equation becomes\n",
        "\n",
        "$$\n",
        "\\psi_{j-1} + \\psi_{j+1} - 2\\psi_{j} = -k^2 h^2 \\psi_j \\; , \\qquad j = 1, \\cdots, N-1\n",
        "$$\n",
        "\n",
        "where $h=a/N$ is the grid spacing, and the boundary conditions are $\\psi_0 = \\psi_N = 0$.\n",
        "\n",
        "Note that the last equation defines the eigenvalue problem in the $N-1$ dimensional space spanned by vectors $(\\psi_1, \\psi_2, \\cdots, \\psi_{N-1})^T$. Here the matrix, whose eigenvalues we are looking for, is tridiagonal, and the allowed values of $(k h)^2$ are its eigenvalues."
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        "Write the function that returns the matrix for the eigenvalue problem above.\n",
        "\n",
        "The numpy function `np.fill_diagonal` may be handy. Also note that to fill sub- and superdiagonals, you may slice the matrix, like so: `a[1:, :]`."
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        "from numpy.testing import assert_allclose\n",
        "def hamiltonian(npts):\n",
        "    \"\"\"Construct the eigenvalue matrix for the discretized 1D Schroedinger equation.\n",
        "    \n",
        "    Parameters\n",
        "    ----------\n",
        "    npts : int\n",
        "        The number of nodes in the mesh: $x_j = a*j /npts$, with $j=0, ..., npts$\n",
        "        \n",
        "    Returns\n",
        "    -------\n",
        "    ham : ndarray, shape(npts-1, npts-1)\n",
        "        The matrix of the mesh version of the Sturm-Liouville operator.\n",
        "    \"\"\"\n",
        "    matr = np.zeros((npts - 1, npts - 1))\n",
        "    np.fill_diagonal(matr[1:, :], -1)\n",
        "    np.fill_diagonal(matr[:, 1:], -1)\n",
        "    np.fill_diagonal(matr, 2)\n",
        "    return matr"
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        "N = 20\n",
        "ham = hamiltonian(N)\n",
        "assert ham.shape == (N-1, N-1)\n"
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      "source": [
        "### Solve the eigenvalue problem\n",
        "\n",
        "Write a function which returns the eigenvalues and eigenvectors of the discretized hamiltonian given the number of the mesh points,."
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        "def eigensystem(N):\n",
        "    \"\"\"Construct the Hamiltonian on a mesh and compute its eigenvalues and eigenvectors.\n",
        "    \n",
        "    Return eigenvalues in the sorted order.\n",
        "    \n",
        "    Parameters\n",
        "    ----------\n",
        "    N : int\n",
        "        The number of nodes in the mesh: $x_j = a*j /N$, with $j=0, ..., N$.\n",
        "        \n",
        "    Returns\n",
        "    -------\n",
        "    vals : ndarray, shape(N-1,)\n",
        "        Eigenvalues, in the ascending order.\n",
        "        \n",
        "    vects : ndarray, shape(N-1, N-1)\n",
        "        Eigenvectors arranged in columns: `vect[:, j]` is the \n",
        "        normalized eigenvector corresponding to `vals[j]`.\n",
        "    \"\"\"\n",
        "    H = hamiltonian(N)\n",
        "    return np.linalg.eigh(H)"
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        "N = 10\n",
        "ham = hamiltonian(10)\n",
        "vals, vects = eigensystem(10)\n",
        "\n",
        "assert (vals[1:] >= vals[:-1]).all()\n",
        "\n",
        "for j in range(vals.shape[0]):\n",
        "    assert_allclose(ham @ vects[:, j],\n",
        "                    vals[j] * vects[:, j], atol=1e-10)\n"
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      "source": [
        "### Long-wavelength limit of the FD problem\n",
        "\n",
        "We expect that in the limit of $N\\to\\infty$ solutions of the discretized system tends to the solution of the continuous problem. \n",
        "\n",
        "Plot the spectrum of the FD problem for several values of $N$. Note that the spectrum is bounded, i.e. we can only hope that low-lying eigenstates match: for large enough $N$, several first eigenstates of the FD problem are close to the corresponding eigenstates of the continuous problem. (See e.g. A.A. Samarski and A.V. Gulin, Sec 1.4.4 for details)"
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        "# Plot the spectrum of the FD problem for several values of N. \n",
        "for k in range(1, 11):\n",
        "    n = 400 * k\n",
        "    val, _ = eigensystem(n)\n",
        "    plt.plot(np.sqrt(val) * n, label=n)\n",
        "plt.plot(np.pi*np.arange(1, n), label=\"original\")\n",
        "plt.legend(loc='best')\n",
        "plt.show()\n",
        "# Plot the spectrum of the continuous problem on the same plot.\n"
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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "vUzHtszf5zsK"
      },
      "source": [
        "The values we get as eigenvalues are $\\lambda_i = k_i^2 h^2$, where $h = \\dfrac{a}{N}$ ($a$ is assumed to be 1)\n",
        "\n",
        "So to get $k_i$ itself we should $\\sqrt{\\lambda_i} * N$\n",
        "\n",
        "Analytically $k_n = \\pi * n$"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "deletable": false,
        "editable": false,
        "nbgrader": {
          "cell_type": "markdown",
          "checksum": "d2f18c2cfac976eecdbe76666433b0e5",
          "grade": false,
          "grade_id": "cell-79c6a06c54de6b6d",
          "locked": true,
          "schema_version": 3,
          "solution": false,
          "task": false
        },
        "id": "9n1qG1RC5zsK"
      },
      "source": [
        "Make the function in the cell below return a value of $N$ such that the first 10 eigenvalues of the FD problem and the continuous problem match within the relative tolerance of $10^{-3}$."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "deletable": false,
        "nbgrader": {
          "cell_type": "code",
          "checksum": "659a5a6782f439c6ec7fa427929c7ab1",
          "grade": false,
          "grade_id": "cell-a0dccf755c881b94",
          "locked": false,
          "schema_version": 3,
          "solution": true,
          "task": false
        },
        "id": "M0k78qD25zsL"
      },
      "source": [
        "def get_large_N():\n",
        "    N = 100\n",
        "    n = 10\n",
        "    eig_origin = np.pi*np.arange(1, n + 1)\n",
        "    eig_comp = np.sqrt(eigensystem(N)[0][:n]) * N\n",
        "    while not np.allclose(eig_comp, eig_origin, rtol=1e-3):\n",
        "        N += 100\n",
        "        eig_comp = np.sqrt(eigensystem(N)[0][:n]) * N\n",
        "    return N    "
      ],
      "execution_count": 8,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "b6VxIXkk5zsL",
        "outputId": "dcee8e94-4964-4a2a-fe50-e1ef519a513a"
      },
      "source": [
        "get_large_N()"
      ],
      "execution_count": 9,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "300"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 9
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "deletable": false,
        "editable": false,
        "nbgrader": {
          "cell_type": "code",
          "checksum": "de871b4813132a85195ec6678c66ddcf",
          "grade": true,
          "grade_id": "cell-d85b44c5d92936e0",
          "locked": true,
          "points": 6,
          "schema_version": 3,
          "solution": false,
          "task": false
        },
        "id": "HkCOsbyA5zsL"
      },
      "source": [
        "NN = get_large_N()\n",
        "\n",
        "vals, _ = eigensystem(NN)\n",
        "\n",
        "# the rest of this cell is a test which compares first 10 eigenvalues\n"
      ],
      "execution_count": 10,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "deletable": false,
        "editable": false,
        "nbgrader": {
          "cell_type": "markdown",
          "checksum": "6cc02a52faa32f2f9407012e912fb88c",
          "grade": false,
          "grade_id": "cell-4a4d614a4c80bf28",
          "locked": true,
          "schema_version": 3,
          "solution": false,
          "task": false
        },
        "id": "v6CVM03F5zsM"
      },
      "source": [
        "### Wave functions"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "deletable": false,
        "editable": false,
        "nbgrader": {
          "cell_type": "markdown",
          "checksum": "938ffede4f4e31402cdb7f7999c5de40",
          "grade": false,
          "grade_id": "cell-fd83c17823e931ad",
          "locked": true,
          "schema_version": 3,
          "solution": false,
          "task": false
        },
        "id": "Oe8ioIja5zsM"
      },
      "source": [
        "Plot the wave functions (i.e. eigenvectors) for several lowest eigenstates. Compare to expected form. How many zeros does the eigenfunction number $k$ have?"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "scrolled": false,
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 1000
        },
        "id": "C3JDt1bq5zsM",
        "outputId": "d79d4cc6-eff2-4985-fdaa-05baf307c230"
      },
      "source": [
        "# plot the wave functions here\n",
        "N = get_large_N()\n",
        "grid = np.linspace(0, 1, N + 1)\n",
        "_, vecs = eigensystem(N)\n",
        "for i in range(5):\n",
        "    k_i = (i + 1) * np.pi\n",
        "    res = np.sqrt(2) * np.sin(k_i * grid)\n",
        "    plt.plot(grid, res)\n",
        "    plt.plot(grid, [0] + list(np.linalg.norm(res) * vecs[:, i]) + [0])\n",
        "    plt.show()"
      ],
      "execution_count": 11,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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4dN44TlU2sq/IcZvd2SqGHwtcXelT2vPaZxBCPCaEOCKEOFJdbZ+zP6WU/G1vMaNDfVmUMspoOSPicxMjmBDpzzN7ix3acwHg1Fa4cg7mftU6A8lthRDqPVTlQfFuo9WMiG6z5LkPzzE1PpiMMcbMhbAUK6bGEBngxTN7i42WMmzs7tBWSvmMlDJDSpkREWGfB6FHLlzhREkdj9w8Fjc7rRQcLFd7Lh+ecVzPBSnho6chZCxMtoP2xyMl7S7wH6XekwOzI7+Si7UtPO7gO2EAL3c3HroxgQ/P1Dhs11lbGfwyIP6qP8f1vOaQPLO3mBBfD+6aET/wxQ5Ar+fy7IeO67lw8SCUHYE5XwaTfba2GBLuXnDD48rDr8w1Ws2w6N0Jjwlz/J1wL/fNGoOvpxvPOeizYiuDvxl4oCdbZzZQL6V0yKTWs9VNvFdQxf2zx+Dj6QSGhU97Lvnl9UbLGR77nwafUJh6n9FKLEfGF8DDD/b/wWglw+Lw+Stkl9TxyE2OvxPuJcjXg7UzR7M5u5zyulaj5QwZS6VlvgYcACYJIUqFEA8LIZ4QQjzRc0kWUAwUAc8C/26JdY3g+X3n8HAz8cDcBKOlWJT7bhiDn6cbz3/ogJN+aoqgMAtmPQqevkarsRw+ITDjQch7C+odb0P87IdqJ7zGSXbCvXzxpgQk8PL+80ZLGTKWytK5V0oZLaX0kFLGSSmfl1L+VUr5157vSynll6WUiVLKNCnlEUusa2vqWzvZeKyMFekxhPvbV7/7kRLk48GaGXFszamgpqndaDlD4/BzYPKAjIeNVmJ5Zj2mso+OvmS0kiFReqWFXQVV3DtrtNPshHuJC/FlccooXj9S4nBFi3Z3aGvPvHW0lNbObh50Mu++l/vnjKGj28zrjtQ6uaMZTrwKySsgIMpoNZYndKxK0zz6kkO1W/hnT8uO+2bb52yIkXL/nDHUtXSyOdux0pm1wR8kZrPkHwcvMG10sMMWjwzE+MgA5iaG8erHF+lylAEpOW9Ae70K5zgrsx5VrSIKNhutZFC0dXbz+uESFiZFERvsY7Qcq3DD2FAmRvnzyoHzDpXOrA3+INlXVENxTTMPzHFOj6WXB+aMoayulV2nHGAMopRw6FmISoP4G4xWYz0SF6h000PPGq1kUGzLqaC2uYMH5iQYLcVqCCG4f04CeWUNHC+pM1rOoNEGf5C8cuACYX6eLElz6ALhAVmYFEV0kDd/P+AA/XUuHoBL+coDdvAc7+tiMsHMR6DkoEOkaL5y8ALjIvy4cbx9DzgZKaumxRLg5e4Yz0oP2uAPgtIrLbx/qoq1s+LtdnyhpXB3M3HfDaPZV1TD2eomo+Vcn0PPgneQKlJydqbdB+4+du/l55TWkV1SxwOzxzh8odVA+Hm5s3pGHNscKNFBG/xB0HsA9W83OHc4p5d7Zo7Gw03Yt+fSWKVi2lM/71ypmP3hEwJpayD3TWi13xDCKwcu4OvpxqoZcUZLsQmfn+1YiQ7a4A9AZ7eZN4+Ucutk5z2AupaIAC8Wp0az4Vip/aadnfgnmLsg44tGK7EdMx+GzhZl9O2QhrZOtuaUs2JqLIHeHkbLsQnjI/2ZMy6MdYcvOsTcW23wB+D9U5eoaWrn3lnOVTwyEPfOjKehrYsd+ZVGS/ksUsKxV2DMTRA+3mg1tiNmGoyaot67HbL5RDltnWaXe1bWzoqnpLaVA8WXjZYyINrgD8C6QxeJCvTicw420WqkzB4XxuhQX/scdH7+Q9UVc/oDRiuxPdMfgMocKD9utJLP8PrhEpKiA0lz0rTl/rg9ZRRBPh6sc4Cwjjb416G8rpUPTldz14x43N1c61dlMgnumRnPweJaztU0Gy3n0xx7BbyCIHm50UpsT9pd4O5td15+Xlk9uWX1rJ0Z7/SHtdfi7eHGndNi2ZFXyZVm+y6Ocy0rNkTWHy3FLOHuDNfaovayZkYcbibBG0fsyHNpqYWTm2HK3eDhGmcqn8InGJJXQu56VWVsJ7xxpARPdxMrp/Y55sLpuWdmPB3dZjYet++eR9rg94PZLHn9cAk3jQ9ndJgLZIH0QVSgN7dMimT90VI67aXyNvdN6G5XTcVclRkPQnsDnHzbaCWAqqzdeLyMJamjCPJ1jcPaa0mKDiQ9PpjXD5fYdeWtNvj98NHZGsrqWrlnpmt6972snRlPdWM7u+2h8lZKOPpyz+FlmtFqjGP0HAgbbzdhne15FTS2dXHPzNFGSzGUtTPjKaxq5IQdV95qg98P6w6XEOzrwaIUJ2zINQTmT4ogMsDLPvKMy4+pylpXPKy9GiHU7+DiAag+bbQa1h0qISHMl9njQo2WYijL0mPw9XSzj2elH7TB74P61k52nqxiRXqM01fWDoS7m4lV0+PYc7ra+GrC7HXg5gWpq43VYQ9MWQvCBDnrDJVRUtvCx+dqWT09zuUOa6/F38udzNRotuVU2G39ijb4fZCVW0FHl5nVLlItOBCrpsfSbZZsPmFgK9iuDnVQOXmpaqfg6gREqaZq2a+D2bjzlU09h5R3TnfNw9prWT09lsb2LnaerDJaSp9og98HG46VMj7S3+XyiftjYlQAabFBbDheapyIop3QWgvp9xqnwd5IXwsNpXBhnyHLSynZcLyM2eNCiQtxzcSGa5k9LoyYIG82HDPwWbkO2uBfw4XLzRw+f4VV02Ndfot6Naumx5JX1kBhZaMxArJfA78ISLzVmPXtkclLwStQhboM4HhJHedqmlk1Xe+EezGZBCunxbL3TA2XGtuMlvMZtMG/ho3HyxACl80n7o9l6TG4m4QxXn5LLRS+A2l3g5u77de3Vzx81KSvk28bkpO/4Vgp3h4mMlNH2Xxte8YuQqD9oA3+VUgp2XCsjLmJYcS4SKO0wRLu78X8SRFsOl5Gt62bROVvAHOnCmFoPk36vdDRBKe22XTZ9q5utmRXcHvKKAJcpFHaYBkfGUB6XBAbjtlfEZY2+Fdx9MIVLta2sGqa3qL2xarpcVQ1tLP/bI1tF85eB5Eprp173x+j50DwaBXysiG7T12ivrVTh3P6YdX0OE5WNFBQ0WC0lE+hDf5VvHWsDB8PNxbrLWqf3Do5kgBvd9t6LjVFUHoY0u9x7qlWw8VkUimaxXugwXYhhLeOlREZ4MWNic491Wq49IZA7a3Vgjb4PbR1drM1p5zM1FH4eek4cV94e7hxx5QY3smrpKm9yzaL5qxT+eZpd9tmPUckfS1Is8365Nc2d7D71CVWTot1uaaCgyXUz5NbJkey8XgZXfbSlgRt8D9hV8ElGtu69BZ1AFZPj6W1s5t38mzQJ99sVnnm4+ZDoHPPEh4RYYkQNwtOvKbaT1iZzSfK6DJLVunc++uyenos1Y3t7CuycQj0OmiD38PG46WMCvRmjt6iXpcZY0IYHeprmzzjiweg/qLOvR8M6WuhukD1yrcyG4+XkRwdyORRgVZfy5G5ZXIkQT4ednV4qw0+UNfSwQenq1k+NQY3k44TXw8hVJ7xgeLLXGqwcp5x7pvg4avyzTXXJ+VOMLmramQrcq6mmezSelZOi7HqOs6Al7sbS6dEs/NkFS0dNgqBDoBFDL4QYrEQolAIUSSE+F4f339ICFEthDjR8/GIJda1FO/kVdLZLVmerv8RD4bl6dFICdtyK6y3SHenyi+flAmeftZbx1nwDVWtFvI3WrXVwtZsdTB8xxT9rAyGZVNiaO3sZleBHXSbxQIGXwjhBvwJyASSgXuFEMl9XPq6lHJqz8dzI13XkmzOLmdsuB8pMXqLOhjGRwaQFB3I5mwrZoUU71GtFFLXWG8NZyN1NdSXQOkhqy2xJaecWQmhuk5lkMwaG0pkgBdbrPmsDAFLePizgCIpZbGUsgNYB6ywwH1twqWGNg4UX2ZZeoxupTAElqVHc/xiHSW1LdZZIO8t1SRt/ALr3N8ZmbxEjT/Me8sqtz9V2cDpqiaWpesD9MHiZhLcMSWGPYXV1Ld2Gi3HIgY/Fri6AXRpz2vXsloIkSOEWC+E6HeqiBDiMSHEESHEkerqagvIuz7bciuQUoUpNINnWc+WfkuOFTyXzlYo2ApJy8Ddy/L3d1a8AmDi7Sqs0235mPGW7HLcTILMNP2sDIVl6dF0dJt5N98GmW0DYKtD2y1AgpRyCrATeLm/C6WUz0gpM6SUGREREdYXll1OUnQg4yMDrL6WMxEf6su00cFsybZCHP/MTuho1H3vh0PqGmiuhvMfWvS2Ukq2ZFcwNzGMcH/9n/BQmBofTHyoj3VDoIPEEga/DLjaY4/ree0TpJSXpZS90zOeA2ZYYN0RU1LbwrGLdXqLOkyWp8dQUNFA0SULd9DMW686YybMs+x9XYEJt4FngPodWpDs0nou1rboxIZhIIRg2ZQY9p+9bPgQIUsY/MPABCHEWCGEJ7AW2Hz1BUKIqy3qcqDAAuuOmK05yjtdpjMOhsXStGhMAjZb0stvb4TTOyB5pe6MORw8fCDpDijYAl2WMy6bT5Tj6WZiUYpuOzIclk+Nodss2W7NzLZBMGKDL6XsAr4C7EAZ8jeklPlCiJ8JIZb3XPY1IUS+ECIb+Brw0EjXtQSbs8uZNjqY+FA9vGE4RAZ6M3tcGFuyy5GWqvA8lQVdbZCms3OGTepqaKuHol0WuV23WbI1p5z5kyII8tGdMYfDpKgAJkT6WycEOgQsEsOXUmZJKSdKKROllL/oee3HUsrNPV9/X0qZIqVMl1LeIqU8ZYl1R0LRpUYKKhr0FnWELEuP4VxNM/nlFuoKmPcWBMapVgGa4TFuPviEWixb59C5Wi41trNMPyvDRgjB8vQYDp2vpbyu1TAdLltpuzm7ApNQYQnN8MlMHYW7SVjmQKqlFs7ugtRVqgukZni4eajBKIVZFhmMsiWnHF9PNxYkRVpAnOvS+x/mthzjvHyXfKqklGzNLmf2uDAiA72NluPQBPt6Mm9iBFuzyzGPdDBKwWYwd+nsHEuQtgY6W+D0OyO6TWe3me25FSxMisLXU5+pjISEcD+mxAVZJ5V5kLikwc8vb6C4pllvUS3E8vQYyuvbOHrxyshulLsewsZDdLplhLkyo+dAQDTkjiyss6+ohistnTr0aSGWTYkhp7SeczW2H0kJLmrwt2SX424SLNYZBxZhYXIUXu6mkZWPN1bC+X3Ku9cVzyPH5KYaqhXthNa6Yd9mS3Y5gd7u3Dwx3ILiXJelU1QIeatBOfkuZ/CllGzNqeDmCeGE+HkaLccp8PdyZ2FSFFm5FcOfd5u/CZA6nGNJUtdAd8ew5922dXbzbn4Vi1NH4eXuZmFxrklMsA+zEkINC+u4nMHPLq2nrK6VpTr33qIsSYumpqmDj89dHt4NTr4NkckQMcmywlyZ2OkQNBpObhrWj+87U0NTe5d+VizMkrRRnK5qsnzB4iBwOYOflVuBh5vgtqQoo6U4FbdMjsDbw8T23GH0C2msVMNOkldaXpgrIwQkL4ezu4cV1snKrSDIx4O5eiiQRclMi0YIyBrOszJCXMrgSynJyq3gxvHhBPnqAhJL4uvpzq2TI9meVzn0sE7BFkCqVEKNZUm5E8ydULh9SD/W3tXNzoIqFiVH4aHn1lqUqEBvMsaEkGVA1a1L/U3mltVTeqWVJTr33ipkpkZT09TO4fO1Q/vB/E0QMRkiJ1tHmCsTO0MVsg0xrPNRUQ2NbV0smaKfFWuQmRrNqcpGzlY32XRdlzL4WbmVuJsEi5J1OMca3Do5Ei9309D6hTRdggsfae/eWgihfrdn31ftFgZJVm4lAd7u3Jios3OsQWaayhC0dW8dlzH4veGcuePDCfbV2TnWwM/LnfmTItieVzn4IiwdzrE+KStVtk7h4IqwOrpU7/bbkqPwdHcZE2FTooN8mDEmhG02juO7zN9mfnkDF2tbWJqmc++tyZK0aC41tg++COvkJgiboDJ0NNYhNgMCYlQm1CDYf7aGhrYu3XbEymSmjqKgosGmRVguY/CzcitwMwluS9YG35osSFJe4aD6hTTXqGKr5BW62MqamEzqd1z0HrQN3ORue24lAV7u3DRBh3OsSe9Zoi0Pb13C4H8SzkkMI1QXW1kVfy93Pjcxgu15FQOHdQq2gDSrkIPGuqSshO52NWvgOnR2m+ShBcMAACAASURBVNlxsrKneloXW1mTmGAfpo0O1gbf0hRUNHL+cguZqXqLaguWpkVT1dDO8ZIBwjon34bQcRCVahthrkzcLNVbZ4BsnYPFl6lr6SQzVe+EbcGS1Gjyyxu4cNk2YR2XMPhZuaoV8u0pOjvHFixIisTTzcS2nOscSDVfhnN7VbGVDudYH5MJkparsE57/6mAWbkV+Hm6MW+i9edJa/6VrbPNRl6+0xv83nDO7HFhhOnhyzYhwNuDeRPDrx/WKdwGsltn59iSlJVqmlg/LZO7us3syK9iQVIU3h46nGML4kJ8SY8PHl6F+jBweoNfWNVIcU2zLrayMUvSoqmob+NEaT8l/fmbICRBt0K2JfGzwX9Uv9k6H5+rpba5Qz8rNmZp2ihyy+q5eLnF6ms5vcHPyq3sCefomKQtWZgchYebIKuvbJ2WWjj3gc7OsTUmEyQtgzM7+5yElZVbga+nG/Mn6XCOLek9W8zKs35YxwUMfgWzxoYSEaDDObYk0NuDmyeoIqzPDDgv3K4mW+lwju1JWQldrZ/J1uk2S3bkV3LL5EgdzrEx8aG+TIkLsknVrVMb/DNVjRRdatIFJAaxJC2asrpWskuvKek/uUm17Y2ZbowwV2b0HPCL/ExY59C5WmqaOvSzYhBL0qLJLq2npNa6YR2nNvjbcisQAm7XKWaGcFtST1jnas+ltU61601ersM5RmBy6wnrvAsd/zIu2/Mq8PYw6XCOQSzpCetst3JYx6kN/vbcSmYmhBIZoAeVG0GQrwc3jg8nK7fiX2Gdwu2qXW/KncaKc2VSVqoB50U7ARXO2Z5Xya2TI/WgcoMYHeZLamyg1XvkO63BL7rURGFVI0u0d28oS9KiKb3SSm5ZT1jn5NuqXW/sDGOFuTJjbgTf8J6xknD0whWqG9t1YaLBLEmL5kRJHWV1rVZbw2kNfu8BSKaOSRrKouQo3E1CFZa01cPZXTo7x2h6wzqnd0BnK1m5FXi5m7h1cqTRylyaT8I6Vjy8dVqDvy23gowxIUQF6nCOkQT7ejK3N6xT+I5q06uzc4wnZSV0NmM+/S7b8yqYPykCPy8dzjGShHA/kqMDrVp1axGDL4RYLIQoFEIUCSG+18f3vYQQr/d8/2MhRIIl1u2P4uomTlU26gISO2Fp2ihKaltpPLZetemNm2m0JM2Ym8A3jCtH1lPV0K6fFTthSdoojl+so6LeOmGdERt8IYQb8CcgE0gG7hVCXNvc/GHgipRyPPBb4JcjXfd6bM9TBx+Zuve9XXBb8igCTW34XtyjsnNMTruxdBzc3GHyHfhfeA9/9y4dzrETekPQ7+RZ5/DWEk/eLKBISlkspewA1gHX7tlXAC/3fL0eWCCElYK4HS1MOPBdvhZ5guggH6ssoRkaoX6ePB59BnfZgUxabrQcTQ/mpJV4mVt4IuY8Ad4eRsvRAIkR/nw9ZD9xH30fujstfn9LBO1igZKr/lwK3NDfNVLKLiFEPRAG1Fx7MyHEY8BjAKNHjx6ymFbpSVp3Pske1u9LoRk8y9wPUyWDueyRgp5tZR+c8EhlrPRnuedho6VormKt+17aWpvpxA1L/zdsd3trKeUzUsoMKWVGRMTQi0B8vNyJnrOW2CuHVM8WjfG0NxF/eR87zDPZnl9ltBpND9vza3hPZhBfvQe62o2WowGoLyO6MYex8+7Fw83y5tkSdywD4q/6c1zPa31eI4RwB4KAyxZYu2+SVyDMXVCYZbUlNEPgzLuIrjbORy1i29VFWBrDUG3DKykdtQjR3qiqnzXGc2qr+pxsnSlwljD4h4EJQoixQghPYC2w+ZprNgMP9ny9BnhfWvOpj54KwWM+KSzRGMzJt8EvgnEzFlJc3czpqv4HcGhsQ05pPWV1rYyemQneQYMecK6xMiffhogkCJ9glduP2OBLKbuArwA7gALgDSllvhDiZ0KI3hO654EwIUQR8C3gM6mbFkUIletdvAdaBxizp7EuHS2qb0vScm5PjUUI20330fRPVm4FHm6ChSnxMPkONZCmq8NoWa5NYyVc2G/VGc8WCRJJKbOklBOllIlSyl/0vPZjKeXmnq/bpJR3SSnHSylnSSmLLbHudUlZqXq2FG63+lKa63DmXdW3JXkFEQFezEoItUkbWE3/SCnZllvBjePDCfL1UM5RW72aUaAxjoItgLRqYaLdHdpajJjpqgWvDusYy8m3Vd+WMTcCsHRKNGcuNXGmqtFgYa5Lblk9pVda/1VsNW4+eAXpZ8Vo8jdB+CSITLLaEs5r8IVQRT5n31fei8b2dPYM2khapgp9gMUpoxACq3cF1PRPVm4l7ibBouQo9YK7F0zKVAeGVsj91gyCpktw4SOrhnPAmQ0+qJNuHdYxjjM7obP5U1vUyEBvZo4J/XSPfI3NUNk5FcwdH06wr+e/vpGyEtrqdFjHKAo2o8I52uAPn7gM1YpXZyAYw8m3wTcMEm7+1MuZaaMo7JlGprEt+eUNXKxtYem1bUfG3QKeAfpZMYr8TRA2warhHHB2g98b1inaBW0NRqtxLTpb4fQ7KgPE7dMF3Yt7ZhS8Y4OhzZpPk5VbgZtJsCj5GoPv4Q2TFkPBVujuMkacq9JU/a9wjpXbhju3wQe1Repu/8zQZo2VKdoFHU19ZhxEB/kwY0wI23Qc36Z8Es5JDCPEz/OzFySvhNZaOP+h7cW5Mqe2gDRbPZwDrmDw42aqlrwndQaCTTn5NviEwNh5fX47M3UUBRUNnKtptrEw1+VkRQPnL7f03wp5/ALw9NdhHVuTvwlCEyEqxepLOb/BN5lUWOfMTmjXqYA2obNNHZRPXgpufbd/6m0Dqw9vbcf23MqecE5U3xd4+MDE21U+uA7r2IbmGji/zybhHHAFgw8qrKDDOrajeDd0NEJy/4PKY4N9mBofzHYdx7cJveGc2eNCCfP36v/C5BXQUgMX99tOnCtzaivIbpuEc8BVDH78bPAfpcM6tiJ/E3gHw7jPXfeypWnR5JU1cPGybmVtbU5VNlJc0zzwZKvxt4GHry7CshX5myBkLIxKs8lyrmHwTSZV/HNmJ7TrVECr0tWuupReJ5zTS2+2Tpb28q3O9twKTAJuTxlgCpynL0xYpMI65m7biHNVWmrh3F6bhXPAVQw+qF9qV5vq7aKxHsV7oL1hUFvU+FBf0uOCdBzfyvT2zrlhbBjh1wvn9JKyEpovwcUD1hfnytg4nAOuZPBHzwG/SJ2BYG3yN6m+LOPmD+ryzLRockrrKanVYR1rcbqqibPVzSyZMshB5eNvA3cf/axYm/xNqo17dLrNlnQdg29y6wnrvKta9mosT1eHarM7eQm495Hn3QdLUq07tFmjMqGEgNtT+snOuRYvf5iwEE5uBrPZuuJclZZa1cbChuEccCWDD+qX29kCRTuNVuKcnPtANaobwhZ1dJgvqbGBuke+FcnKrWBWQiiRAd6D/6HkldBUCSUfW0+YK1OYBeYum4ZzwNUM/ui5qlWvzkCwDvmbwCsQEm8Z0o9lpkZzoqSOsrpWKwlzXc5UNXLmUhNLBxvO6WXi7eDmpcM61iJ/EwSPhphpNl3WtQy+m7sK65zeoXq9aCxHd6c6hJqUqdrtDoHeVEE9GMXyZOVWIoRqSz0kvAJgwm3K4OuwjmVpvaKSG5JX2DScA65m8EH9kjuboeg9o5U4F+c+UO11h7FFHRvuR1J0INt1HN/iZOVWMHNMKJGBQwjn9JK8AhrLoeyI5YW5MoXbVdv26xQmWgvXM/gJN6uWvfkbjVbiXORvUu11E28d1o8vTRvF0QtXKNdhHYtRdKmJwqpGMq9thTxYJi4GN0/9rFia/E0QFA+x022+tOsZ/N6wTuF26NCNuyxCV7sa4DB5iWqzOwyWTokBYFuODutYii3Z5QjBwNW1/eEdqFI08zfqIixL0VILZ3fZPDunF9cz+ACpa1S2zul3jFbiHPSOkUxdM+xbjA33Iy02iC055RYU5rpIKdmSXc7ssWFEDSec00vaamis0EVYlqJgs8rOGcGzMhJc0+CPmQsB0ZC3wWglzkHuetUKeYjZOdeyPD2GnNJ63TLZAuSXN1Bc08zyqTEju9HExaq3Tu56ywhzdfLeUq2QbVhsdTWuafBNbpBypyrCaq0zWo1j09GscoqTVwzYO2cgelMHt2ZrL3+kbMkux90khp6dcy2efjBpicrW0QPOR0ZjJZz7ENLWGBLOAVc1+KC2VN0dcGqb0Uocm9PvqPCYBbaoMcE+zEoIZXN2OVJKC4hzTcxmydacCuZNjOh7stVQSV2tJmEV7xn5vVyZ/E2AVL9Pg3Bdgx87HUISIE9vVUdE3gbVenrMXIvcbll6NGd6sks0w+PYxSuU1bWyLH2Yh7XXMn4BeAepcIRm+OSth6g0iJhkmATXNfhCqP9piz9QQ4Q1Q6e1ToXFUlepMJkFyEyLxs0k2HxCh3WGy5bscrzcTdx27aDy4eLupTLbCrbqgsXhcuU8lB5Wz4qBjMjgCyFChRA7hRBnej6H9HNdtxDiRM/H5pGsaVFSV6v2pHowyvA4tU2FxSy4RQ3392JuYhhbcnRYZzh0dZvZllvBgqRI/L3cLXfj1DVqitkZ3YdqWPQmiBgYzoGRe/jfA3ZJKScAu3r+3BetUsqpPR/LR7im5YhKgYgkna0zXPLWq/ausTMsetvl6TGU1LZyokQfqA+Vg8W11DR1sDx9hNk515JwM/hF6BDocMnbAHEzIWSMoTJGavBXAC/3fP0yYNvWb5YgdbWa31lfZrQSx6KpWoXDUldbPONgUcooPN1MbMnWRVhDZUt2Of5e7syfFGnZG7u5q7YZp3dAuz5fGRLVhVCVa7h3DyM3+FFSyt6nshLor+G2txDiiBDioBDiuv8pCCEe67n2SHW1DWLrvTG1fO3lD4mTm1Q4LM3yBSRBPh7MnxTB1pxyus06rDNY2ru62Z5XwaKUKLw9LHOm8inS1qipcaeyLH9vZybvLUCoVHCDGdDgCyHeE0Lk9fGx4urrpAq49vd0jpFSZgD/BvxOCJHY33pSymeklBlSyoyIiIihvJfhEZaoWpTqDIShkbcBIiZDZLJVbr8sPYZLje0cOldrlfs7Ix+erqGhrYtllg7n9BI3CwLj9LMyFKRUv6+EmyDAQofoI2BAgy+lXCilTO3j422gSggRDdDz+VI/9yjr+VwM7AFs2wR6IFLXQPlxuHzWaCWOQX2pCoOlWq+AZEFSJL6ebmzWRViDZnN2OSG+Htw0Ptw6C5hMakd8dpfqCaMZmIpsuFxklZ3wcBhpSGcz8GDP1w8Cn5mWIIQIEUJ49XwdDtwInBzhupYl5U5A6MPbwdLbPdGKKWa+nu4sTIpie14Fnd26H/tAtHR0sfNkFZlp0Xi4WTHbOnW16gVTYD/JdnZN3ltgcock+8hVGem/jKeA24QQZ4CFPX9GCJEhhHiu55ok4IgQIhvYDTwlpbQvgx8UqwqHcl5XWzDN9cl5Q4XBwvqNzFmE5ekx1LV08kGhrpMYiJ0nq2jt7LZ8ds61RKdD2Hj1b0BzfczdyuAnLgDfUKPVACM0+FLKy1LKBVLKCT2hn9qe149IKR/p+Xq/lDJNSpne8/l5Swi3OFPugctnoPyY0Ursm6p8qMyBKWutvtS8iRGE+nmy8bjOoBqIDcfKiO1pTWFVhFB/9xc+gisXrLuWo3P+Q2gog/R7jFbyCa5baXstKSvVDM/sdUYrsW+y16ktqg1SzDzdTSxPj2FnQRX1LbpxV39camjjwzPV3DktFpPJBk25ptytPmsv//pkrwOvINV8zk7QBr8X7yCYvFS1ge3qMFqNfWLuhtw31VAMfxtkUAGrpsfS0aWqRzV98/aJcswS7pwea5sFQ8aoQqzs13QItD/am+DkZuVIevgYreYTtMG/mvR7VVfAIl0+3ifnPlDDMNKtH87pJS02iPGR/mw8XmqzNR2Nt46VMjU+mMQIf9stmr4Was9CqZ532yentqrZ2en3Gq3kU2iDfzWJt6ry8ezXjFZin2SvUzuhiYtttqQQglXTYzl8/goXLuvBKNdysryBU5WNrLaVd99L0nJw99HPSn9kv6bajoyebbSST6EN/tW4uUPa3VD4js4zvpb2RijYAimrhj23drisnBqLEOjD2z7YcKwUDzfBHVOsnJ1zLd6BkHSHykLparft2vZOfZlqO5J+r2GDTvpDG/xrSV8L5k7dauFaCraoQScGbFFjgn2YmxjGhmNluoPmVXR1m9l0opxbJ0daZtDJUElfC211qr+O5l/kvgFIu8rO6UUb/GsZlQaRKTpb51qyX4OQsRA/y5DlV02L42JtC0cvXDFkfXvkw6IaapraWTU9zhgBY+er4Tf6WfkXUqrfR/xsCB1ntJrPoA3+tQihPJfSw1BTZLQa+6CuRM3iNHCLujh1FD4ebrx1TId1etlwrIxgXw9usXRnzMHi5g5T7oIzO6D5sjEa7I2KE1B9yqaJDUNBG/y+SLsLhAlytOcC/GuL2pt/bQB+Xu5kpo5ia045bZ3dhumwFxraOnk3v5Ll6TF4uhv4GKffq1ot6IZqiux1qp4nxT47xWuD3xeB0TDuFjjxmso9d2WkhBOvwui5EDrWUCmrpsfR2NbFuyerDNVhD2zLqaC9y2xcOKeXqBQVBj3xD2N12ANd7apOZVIm+PQ5/M9wtMHvj+n3Q0MpFO82WomxXDyguv1Nv99oJcxNDCM22Ic3DpcYLcVw1h0uYVJUAOlxQUZLgWkPqK6QFdlGKzGWwixouWwXz0p/aIPfH5OWgG8YHHvFaCXGcuwV8AqE5BUDX2tlTCbBPTPj2VdUQ0lti9FyDKOgooHskjrumRmPsIe0vyl3qTDGsb8brcRYjr0CQfEqOmCnaIPfH+5eKj55KkuN83NFWusgf5Pq5e3pZ7QaANbMiMMk4HUX9vJfP1yCp5uJO6fZuNiqP3xClEOQ8wZ0thqtxhiuXICzu2Ha58FkhWljFkIb/Osx7X6Vk++q1YS5b0JXK0x/wGglnxAT7MPnJkbw5tESulywT35bZzcbjpVye+ooY3Lv+2P6A9Ber/rHuCIn/qk+T73PWB0DoA3+9YicDPE3qK2aKxb8HHtFHchFTzVayae4Z+Zoqhra+eC06+28duRX0tDWxdqZ8UZL+TQJN6m8c1cMgZq74fg/YPwCCLazv5dr0AZ/IKY/qPrkXzxotBLbUn5C9b2f/qDdlYcvSIok3N+LdS4Y1ll3qITRob7MGRdmtJRPI4TaEV/Y53r1K2ffV33v7Wgn3B/a4A9EykrwDIBjLxutxLYcewXcvVVNgp3h4WZizYw43j91iUsNbUbLsRnna5o5UHyZe2bG26bv/VCZ+m8g3OC4i3n5x14G33CYmGm0kgHRBn8gPP1UFkL+RtdpqNbeqA7gkleCT7DRavrknpnxdJulS3n5rx66iJtJsGaGwbn3/REwSuWgH/+n6zRUayhXiR1T7wV3OzpT6Qdt8AfDzEegq03F6VyB7HXQ0QizHjVaSb+MDffj5gnhvPrxRZc4vG3r7OaNIyXcnhJFVKBtu5UOiZkPQ0uNyu5yBY6+BNIMGQ8brWRQaIM/GKJSVKXpkeedv/JWSjj8nDqojZ1htJrr8sCcBCob2tjpApW3m7PLqWvp5P7ZCUZLuT5j56sh54efNVqJ9enqUAZ/wm2GV6EPFm3wB8usR+DKeSh6z2gl1uX8PtX8adajdndYey23To4kNtiHlw+cN1qKVZFS8sqB80yM8mf2OCsPKR8pJpPaEZcehvLjRquxLqe2QFMVzHrMaCWDRhv8wTJ5mWoFe8jJPZdDz6hCGhsMKR8pbibB52eP4WBxLaerGo2WYzWOl9SRV9bA/XMS7KOydiDS7wUPPzj0nNFKrMuhZ1XL8MQFRisZNNrgDxZ3T5jxkPLwa4uNVmMd6svg1DaVXmdHg5evxz0z4/F0N/H3AxeMlmI1/n7gAv5e7vZTWTsQPsGqs2reeudNdKjMU32mZj6sdjUOguMotQdmPKTKpg8/b7QS69B7ADXTMQ6gAEL9PLljSjQbjpXS2NZptByLU9PUzracClZPj8Xfy91oOYNn1qPOnehw+Fk109fOK2uvRRv8oRAYDUnL4PjfVeqiM9HZBkdfhAmLICTBaDVD4sE5CTR3dPPmkVKjpVicVz++SEe3mfvnjDFaytCISoExN6qwR3eX0WosS0utSltOWwO+dn6mcg3a4A+VOV+Btnrn81xy1kFzNcz9itFKhkx6fDAzE0J4ft85p0rRbOvs5uX957llUgTjIwOMljN05nwZ6i9CwdtGK7Esh59X853nfNloJUNmRAZfCHGXECJfCGEWQmRc57rFQohCIUSREOJ7I1nTcOIyYPQcOPBn5/FczGbY/0eIToeEm41WMywevXkcZXWtbM+rNFqKxdh4vIzLzR08Os/+ZqMOiomZKkXzo6edpxdVZxsc+pvaCUcmGa1myIzUw88DVgF7+7tACOEG/AnIBJKBe4UQySNc11jmfk15LiedpLjk9DuqX9Dcr9l9KmZ/LEyKYly4H8/sLUY6gXExmyXPflhMWmyQ/fXNGSwmk9oRV5xQ6b7OwCc74a8arWRYjMjgSykLpJSFA1w2CyiSUhZLKTuAdYDx0zRGwsTFEDYB9juJ57L/aQgarVopOCgmk+CRm8eRW1bPwWLHzwzZdeoSxdXNPDpvnGOkYvZH+lrVZ2b/00YrGTmf7ISnOuxO2BYx/Fjg6oYnpT2v9YkQ4jEhxBEhxJHqajttf2syqVh3RTac/9BoNSOj5LBKL5vz7+DmQFkgfbBqeizh/p48s/es0VJGzDN7zxIb7MOS1FFGSxkZHj5ww+Nw5l24VGC0mpFxenvPTvirDrsTHtDgCyHeE0Lk9fFhFS9dSvmMlDJDSpkRERFhjSUsw5S14Beh4pOOzP7fg3eQyr13cLw93HhgTgK7C6sduhDr2MUrHD5/hYdvGou7mxPkVWQ8rFIY9//BaCUj4yMn2AkPdIGUcqGUMrWPj8EevZcBV08FiOt5zbHx8IYbnoCinVB2zGg1w6PqJBRsVaXwXv5Gq7EI988eg6+nG39433F7sv9h1xmCfT24x96GnAwXvzDVKz7nddWexBE5txdKDqrMHAfeCdvCfTgMTBBCjBVCeAJrAeeYgzbrMdWGYM9TRisZHh/8Ejz91cGakxDi58mDcxPYmlPukF7+8YtX2F1YzaM3j8PPkQqtBuKmb6he+Xv/z2glQ0dK2P0/qrXKjAeNVjMiRpqWeacQohSYA2wTQuzoeT1GCJEFIKXsAr4C7AAKgDeklPkjk20neAcqY3lmB5QdNVrN0KjKV1lGNzzucMUjA/HYzePw9XDj6V1njJYyZH6/6wwhvh48ODfBaCmWJTBGVaqfeBVqzxmtZmic2wsX98PN33KYliP9MdIsnY1SyjgppZeUMkpKeXvP6+VSyiVXXZclpZwopUyUUv5ipKLtCkf18vc8BV6BDlk8MhAhfp48dGMC23IrHMrLP3bxCnsKq3l03jjHaqMwWG76Jrh5OJaXLyXs+R8IiFHjPh0cJzgRMhjvQHVqf+ZdKD1itJrBUZkHBZvVGYSTefe9PHrzOPw83fn9e47j5f/uvTOE+nny4JwEo6VYh8BomPEFyH7NcRoQFu9RWWw3f0ud2zk42uBbglmPgU8o7H7SaCWD44OnwCtIpWI6KcG+nnyhx8svqGgwWs6AHL1Qy97T1Tw2z8li99dy0zeUl//B/xqtZGB6vfvAWIcYUD4YtMG3BF4BcOPX4ewuFe+zZ0oOQcEWZex9QoxWY1UeuWkcAd7u/OqdU0ZLuS5SSp7afopwf08ecLQmaUMlYJTKCstZp86R7JnCLCj5GG7+Nrh7Ga3GImiDbylueByC4mHHD1VFnj0iJbz7I/CPcqrMnP4I8vXgq7eOZ3dhNfvO1Bgtp1925Fdx+PwVvnnbRHw9ndi77+XmbysnaeePjVbSP92dSl/4RKfx7kEbfMvh4QMLfgyVOZD7htFq+ubk28pjueWHTpN3PxAPzEkgLsSHX2QV0G22vzYYHV1mntpewIRIf+7JcJK8+4HwDYV531HDhIp2Ga2mb46+BJeL4LafqRCUk6ANviVJXQMx02DXz6Cj2Wg1n6azDd77CUQmw7TPG63GZnh7uPGdxZMpqGhg/dGSgX/Axvz94AXOX27hB0uSnKOqdrDMelTNXXj3R/bXdbb1iordJ9ys+mY5ES70L8wGmEyw+JfQUAYf/MpoNZ/mo9+pKsfbn1RTu1yIZVOiyRgTwlPbT3GlucNoOZ9Q1dDGb3ee5nMTI5g/yY7biFgDdy9Y9HO4dFK1G7Yndv23Mvq3P+mwPXP6Qxt8SzP6BuVBH/gjXLKTw8LLZ+HD36jB5Im3GK3G5ggh+O+VqTS0dfGrHQM1d7UdP99WQEe3mf9anuLYHTGHy+Q7VF/53U9CQ7nRahRlR+HICzDrcYieYrQai6MNvjVY+F+qZcG2bxt/gCslZP0nuHnCIueqeRsKSdGBfGFuAq8dusjRC1eMlsO+MzVsyS7n3+cnkhDuZ7QcYxACMn8F5i545/tGq1Ghpa3fUkkNt/zAaDVWQRt8a+AXrg57LuyDIwYPPD/xT5UueuuPVOGLC/ON2yYSHeTNd9Zn09bZbZiOxrZOvvtWDmPD/Xjic4mG6bALQsfCvP9QbT5OGjwKcf/TaljL4idVQaUTog2+tZj+ACTeqlK7jKoqrCtRntOYm1RxmIvj7+XOL1dP4Wx1M79+17jQzpNZBVTUt/J/d03B28O1zlP65MZvqKEiW78JTQbNwKjKVwe1ySsgZZUxGmyANvjWQghY/kcwecDGL9k+E8Fshre/DOZuWPFHdaCsYd7ECO67YTTP7TvHx8WXbb7+7sJLvHaohEfnjWPGGOdsazFk3Dzgzr9CeyNs+brtp8h1tcPGJ1RvqaW/cbqDLOahJQAAClpJREFU2qvRVsCaBMXC0v9TfbT32Ljtwoe/hnMfwO2/UNtmzSf8YEkSY0J9+fq6E9Q0tdts3fK6Vr71+gkmjwrgmwsn2mxdhyAySdWxFG6Dj22ctfPuj1T9zPKnVTjWidEG39pMuVt12fvw11D4jm3WPLsbdv8C0u5WLWk1n8LPy50/3TedKy0dfH3dcZsUZHV0mfnyq8fo7Jb8+b7pOpTTF7O/DJOWwLs/VC1AbEHuejj0jKo8n7zUNmsaiDb4tiDzVzBqCmx8DKpPW3et2nPw1iMQMQnu+K1Tb09HQkpMEP+9IpWPii5bvdeOlJL/2pLP8Yt1/HL1FMZFuEaV85AxmWDln1WzsjcetH6qZkUObP4axN8AC39q3bXsBG3wbYGHN9zzd5Ua+c/V0FhlnXWaa+Afq0F2wz3/cJn2CcPl7pnx3D97DH/bW8zL+89bbZ0/7znLPz++yBOfS2TpFNfOlBoQnxBY+08Vz//HGmirt846dRfhn2vAJxjuesmp2idcD23wbUVIAvzbG9B8Wf1Da7VwLnhbA7x6j6ryvfd1CJ9g2fs7KT9dnsJtyVH8dEs+W7It71G+cbiE/91RyMqpMXzn9kkWv79TMioN7nkFagph3X3Q0WLZ+zdVK8eoqw0+/5aaxuUiaINvS2Knw92vQPUpeOkOaLpkmfu21MIry1UO8ernVbWvZlC4mQRPr53GzDGhfH3dcd48Yrl+O68cOM933srh5gnh/GpNOiaTDq8NmsRbYeVf4MJHyjhbytOvL4UXF6vPa19Th8UuhDb4tmbCQuXp1xbDC4tHHtO/fBZezISqk7D2VUi6wzI6XQgfTzde+uJMbhwfzn+uz+Eve84iR5Aa2G2W/ObdQn78dj63JUfx7AMZeLrrR23ITLlbOTClh+DlZaquZCRU5sILmcrRun8jJNxoGZ0OhP5XaASJt8D9m6CtDp6ZDzlvDu8+Jzern2+shM+vh4m3W1KlS+Hr6c5zD2awdEo0v3znFI++cpT6ls4h36emqZ2HXjzE0+8XcdeMOJ2RM1JSVylP/HIx/O1mOLNz6PeQEo69As8thO4OeHALjJ5tea0OgBiJJ2NtMjIy5JEjDjIndjg0lMObX1B5+uNvU935IgaRn335rModLsyCmOnq0CnEyScl2QgpJS9+dJ4nswoI8vHg24smcc/MeNwGCMd0dpv5x8EL/O69M7R2dvNfy1NYOzPeNZuiWYOaInjzQajKg5Q7VeuS4NED/1xlHrzzPTj/IYybD6ueA3/n7kwqhDgqpczo83va4BtMdyd8/FfVTrmjSRn+qf8Go+dAQNS/rmuqVv8xnHgNTr+jBq7c/C2VP+wk49fsibyyev5rSz6Hz18hLsSHu2bEsyglivGR/nj09K3v6DJzuqqRHfmVrD9aSkV9GzeND+fHy5KZGBVg8DtwQjpbYd/v4KPfq4Zrk5dA+r0QNwv8wtQ1Uqod74WPevpI7VaZOPN/ADMfdonW4NrgOwJN1XDwz3DiVWiqVK/5hoG7j8omaOkZ0ecXCelrYc6X1XxQjdWQUrIjv5J/HLzIviL1+/d0NxHm5wmo8E1nt8QkVMuGB+aM4ZZJkdqrtzZ1JepZyXkdWnraY/hFqrTnzhZorVWvBcXD1PvU+FFf12ljoQ2+I9HdpcYQVmSrbB5ztypICZ8E0ekq9ugiOcP2RFldK0fO15Jf3vDJEJVQf09SY4KYmRDKqCBvgxW6IF0dcHG/elZqzijv3s0dIpLU5Lm4DJfw6K9FG3yNRqNxEa5n8HWWjkaj0bgIIzL4Qoi7hBD5QgizEKLP/1F6rjsvhMgVQpwQQmiXXaPRaAzAfYQ/nwesAgbTz/QWKWXNCNfTaDQazTAZkcGXUhYAOitBo9FoHABbxfAl8K4Q4qgQ4rqz9oQQjwkhjgghjlRXGzTuTKPRaJyQAT18IcR7QF8J3z+UUg526vBNUsoyIUQksFMIcUpKubevC6WUzwDPgMrSGeT9NRqNRjMAAxp8KeXCkS4ipSzr+XxJCLERmAX0afA1Go1GYx2sHtIRQvgJIQJ6vwYWoQ57NRqNRmNDRlR4JYS4E/gDEAHUASeklLcLIWKA56SUS4QQ44CNPT/iDrwqpfzFIO9fDVwYprxwwNWygvR7dn5c7f2Cfs9DZYyUss8OcXZdaTsShBBH+qs2c1b0e3Z+XO39gn7PlkRX2mo0Go2LoA2+RqPRuAjObPCfMVqAAej37Py42vsF/Z4thtPG8DUajUbzaZzZw9doNBrNVWiDr9FoNC6Cwxt8IcRiIUShEKJICPG9Pr7vJYR4vef7HwshEmyv0nIM4v1+SwhxUgiRI4TYJYRw+OnmA73nq65bLYSQ12vV7SgM5j0LIe7u+bvOF0K8amuNlmYQ/7ZHCyF2CyGO9/z7XmKETkshhHhBCHFJCNFnIapQPN3z+8gRQkwf8aJSSof9ANyAs8A4wBPIBpKvuebfgb/2fL0WeN1o3VZ+v7cAvj1ff8mR3+9g33PPdQGodh0HgQyjddvg73kCcBwI6flzpNG6bfCenwG+1PN1MnDeaN0jfM/zgOlAXj/fXwJsBwQwG/h4pGs6uoc/CyiSUhZLKTuAdcCKa65ZAbzc8/V6YIFw3H7OA75fKeVuKWVLzx8PAnE21mhpBvN3DPDfwP9v735CbArDOI5/fxqy8K/MRkyNhSk1FsqCFUWSxbWxoCZGkx0LycqC7CR2SonEQrHRLWo2kpIps2WhCY3Byp/ZiAw/i/csJsl9p3vvuc69z2d1zul07/Pcc89zz/s+t3POA9/KDK5NcnI+Cly2/RnSfapKjrHVcnI2sKJYXgm8LzG+lnO6geSnf+yyD7jpZAJYJWlNM+9Z9YK/Fng7b32m2PbXfWzPAbPA6lKia72cfOcbI10hVFnDnIuh7oDt+2UG1kY5x3kIGJL0RNKEpD2lRdceOTmfBUYkzQAPgOPlhNYxCz3fG2r2iVfhPyVpBNgCbO90LO0kaRFwCRjtcChl6yNN6+wgjeIeS9pk+0tHo2qvg8AN2xclbQNuSRq2/avTgVVF1a/w3wED89bXFdv+uo+kPtJQ8GMp0bVeTr5I2gWcBmq2v5cUW7s0ynk5MAw8kvSGNNdZr3jjNuc4zwB12z9svwZekn4Aqion5zHgDoDtp8BS0k3GulXW+b4QVS/4z4ANktZLWkJqytb/2KcOHC6W9wMPXXREKqhhvpI2k54xXOuCeV1okLPtWdv9tgdtD5L6FjXbk50JtyVyvtf3SFf3SOonTfG8KjPIFsvJeRrYCSBpI6ngd/Nj8erAoeLfOluBWdsfmnnBSk/p2J6TdAwYJ3X5r9t+LukcMGm7DlwjDf2mSA2SA52LuDmZ+V4AlgF3i970tO1ax4JuUmbOXSUz53Fgt6QXwE/glO2qjlxzcz4JXJV0gtTAHa3wxRuSbpN+tPuLvsQZYDGA7SukPsVeYAr4Chxp+j0r/HmFEEJYgKpP6YQQQsgUBT+EEHpEFPwQQugRUfBDCKFHRMEPIYQeEQU/hBB6RBT8EELoEb8Bz+PUtW0jCl8AAAAASUVORK5CYII=\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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X104krfRDhImheu8vbEdRs6AF/woZbbupjFoRUEvVTlXhDQ/gMkLHYZ0+F6hM5StcJIGidbfajjJtBSs300YqEdV6kV8w04Lv0d5Uw2JXPZcWBd8vI0DKgiyqIpaQ0rLHdhQ1DpfTSX7vQWoSNhIWHm47zrSJw0FDyvUU9h3WxdSCmBZ8j4aD7jc809d+0HKSmbuw8CaKRivp7myzHUVdpbr8HVLohcLAXq7jWiKK7yBeBqk6rHPyg5UWfI/w2jc4Twp5SwN3sbTJJK/ajkMM1Qd1tk6g6Sp/yX117abguL5jPEWbPsCoCaPnhE7/DVZa8IHRkWGK+g5Rn3x9UFxdO5Gi1VvpJg5zVqfPBZrk5t1URxSRsmDcO3sGhfjEFM5GlbCg/R3bUdQMBW9186KqI7uIl0HCi4Pn6sfxhIWHUxO/gcU9B3V1wwDS09VO0egZLmTcaDvKrPVmbaXAWUtnS4PtKGoGtOADPSdeZsw4KAzil9uXuQq2kUo3tSf3246iPKoPvEiYGJJWBdf1HeNZsNb9O1J7cIflJGomtOADaW1vczayhISk+bajzNriTfcC0HlU+6yBwlW1kx5iKVpzs+0os5a/fAMdJBNWs9N2FDUDIV/wO9vOUeisoSd7q+0oXpGakUN1WAGJzW/ZjqJwT8dc3L2f6vgNQTkd82ricFCXtJnCvkOMjY7YjqOmKeQLft0B94yWtNUfsJzEezoybqRo5LTeFCUA1FUcJJVunPm32Y7iNWFLtpFIP9XH9JqPYBPyBd9Rs5NOkihYudl2FK9Juu5uwsVFzQGdnmnb+aPuG4Dnb7zXchLvKdx0L04jdJdr2zDYhHTBdzmd5F86RF3ihqCejnm1orW3cMnMY6zqDdtRQl5C89vUOvJIzcy1HcVrElPSqIpYSnKbTs8MNnOnys1AXcVBkrkE+cG3euG1hEdEUh27hqyL79qOEtIG+y9RNHyK82lz59XjZd0Z11M4epbe7i7bUdQ0hHTB7zjuXggqb33wT5e72nDOFrJMOy11Z2xHCVnVh3cSKWPMWzp3+veXxZdsI0wMNe++bDuKmoaQLvgxTXtpcOSQlplnO4rXLVx9FwBNR/QX0pa+0zsZMWEUlgb3BX3jKVx7MwMmipGqXbajqGkI2YI/MjxE4eBx2uZvtB3FJxYVr3HPl67XmRS2pJ4/QHVUCbHxSbajeF1UdAzV81aS0XXQdhQ1DSFb8KuP7CJGhoksmlv9+8vE4aAhoZTFl8p0mQULerraKRiroSfjettRfGYgewu5rkY6WuptR1FT5JWCLyJ3iUiliFSLyFfHef5TItIhIsc8H3/gjXFno7fidZxGKNiw3XYUn3Et3koKvdSfLrMdJeTUHHoZhxiSV8y9ds5lqSvvAKD+kE7PDBazLvgiEgb8ANgOlACPiEjJOJs+Y4xZ7fn48WzHna2k9v1URyyZE8spTGRRqfs/s/Plr1hOEnpGq3bRb6IpWH2T7Sg+k79iExeJh9rdtqOoKfLGGf4GoNoYU2uMGQGeBu7zwn595lLPBQpHznAhfe6+3AbIyCmkUTKZ16Tzpf0t88K7VMWsJiIyynYUn3GEhVEXt5bcnncxLpftOGoKvFHws4DGKz5v8nztah8WkeMi8pyI5Ey0MxF5TETKRKSso6PDC/Her+bQq4SLi/iSuTdd7mot8zdRNFDOyPCQ7Sgho+1cFTmmhaGcLbaj+Nxo7lYWcIFzVcdtR1FT4K83bV8E8owx1wGvA09MtKEx5nFjTKkxpjQtzTc3Ex86+yaDJpLCtcF5/9rpiCi6lRgZpuaYvuz2l3OH3VNh0z1TY+ey7HXua1jajmnbMBh4o+A3A1eesWd7vvYeY0yXMebynY9/DFi9j2BG5wGqo1cQPS/WZgy/KFh/l3vdk5N6Fyx/cdTtppOkoL5d5lRl5S+jRRYQ2aDTf4OBNwr+IaBIRBaLSCTwMPA7d0cQkYVXfHovcNoL485IZ9s58lzn6M+a+y+3wb3uSU1EEUlt+2xHCQnG5SKvt4z6hNI5tT7TtTQlbaBg4CjOsTHbUdQkZv0TaYwZA74AvIq7kD9rjKkQkW+IyOUlAr8kIhUiUg58CfjUbMedqfp33VPI5l93h60Ifte1YBOFI2fov9RtO8qcV3/mMKl0Y/Lm7uycqzkKbyaBAWqO6+SAQOeVUxBjzEvGmCXGmAJjzDc9X/uaMWaH5/H/MsYsN8asMsbcYoyxtsCLq3Y33cSRv2LuLWg1kfhl24gQJ9WHXrMdZc5rP+ZenymndO6tzzSRxZ7pv10n9Ocr0IXGa04P43KxqPsQtbFr58Tdh6aqsHQbwyaCwUpdLtnXopveoUkWkrGoyHYUv5mfnk2tI4/4lr22o6hJhFTBb204SwYdjC66wXYUv4qeF0t11DJSOw/ZjjKnOcfGyB8opyW51HYUvzufuoGCoVMMDw3YjqKuIaQKftMx90yVBSvn/vz7q/VmbCJ/rFZve+hDdRUHSWAAR15oTAi4UlThVubJCLXlb9uOoq4hpAq+1L/DRRLILV5rO4rfJSy9BYcY6g7r9Exf6TzpbpnlrJ276+dMJH/d7biM0H3qTdtR1DWEVMHP7jlMXexqHGFhtqP4XcGarQybCIaq9AIsX4lq3k+TZJCeXWA7it8lzk+nLjyP+LYDtqOoawiZgt9SX8lCOhjJDp3ZOVf6bR9fb3voCy6n092/Twy9V4+Xdcxfr338ABcyBb/Z079Pvy70+veXaR/fd+pOHSKRfmTxjbajWKN9/MAXMgWf+ne4SDy5S0NvBsVl2sf3nY7L/fs1ode/v0z7+IEvZAp+Vs8R6mNXhWT//jLt4/tOVNM+WiQ9pObfX037+IEvJAp+a0Mlmaad4ey5vf79ZLSP7xsup5O8/nKaQ7h/f5n28QNbSBT8pqM7AUhbEbr9+8u0j+99DWfKSOYShOD8+6tpHz+whUTBN/Xv0EMsi0vW245infbxve/8CXfPOmt16PbvL9M+fmALiYKf1XOY2pjQnH9/Ne3je19E4z5aSSMzr9h2FOu0jx/Y5nzBb2usJsu0Mxyi8++vpn187zIuF3n9x2jS/v17tI8fuOZ8wW866m5daP/+t7SP7z3nKo+SQi/khtaCfNcSWXCT9vED1Jwv+K66t939++UbbUcJGNrH95624+4JAZmrQ+eGOpPJX+d+L0P7+IFnzhf8zO4j1MaE9vz7q2kf33vCG/fRznzt318hKTXDvT6+9vEDzpwu+O1NNWSbVoaztH9/Je3je4dxucjrO0pjwtqQuX/tVJ3XPn5AmtM/pY1H3C2L1BW3Wk4SeLSPP3vnqo4znx5c2r9/n0idjx+Q5nTBd9W/Qy8xLF6+yXaUgKN9/NlrK3f/3WWu0vn3V9M+fmCa0wV/4cXD1MasCqn7106V9vFnL7xxH+dJISu/xHaUgKN9/MA0Zwt+R0s9OaaFoUw9ux/P5T7+fL3P7YwYl4tFl45yTvv3E7rcxx8ZHrIdRXnM2Z/UhiOvATBf599PqDd9I/ljNfR2d9mOEnSaak6QxkWcOaG9IN+1RBXe6O7jH9tjO4rymLMF31n7NpfMPPJX6AydicQv3UqYGOqOaB9/ulrL3evfZ67eZjlJ4Mpb6742ofv0W3aDqPfM2YKfebGM2pjrtH9/DYVrbmHEhDN4Vs/Apstxbi+dJJFdsNJ2lICVnLaQOkcusa37bUdRHnOy4He2NJBjWhjU+ffXFB0TR3XkUlK0jz8txuViUe8RGuK1fz+Z8ynrKBiqYHRk2HYUhZcKvojcJSKVIlItIl8d5/koEXnG8/xBEcnzxrgTqT/q7t+nlOj8+8n0pm8kf7SaSz0XbEcJGs21p1jABca0fz+piIKbiJFhao6/YzuKwgsFX0TCgB8A24ES4BERuXqe2meAi8aYQuA7wLdmO+61OGvfoc/MI3+lnuFPJq54K+HiovbIG7ajBI2Wcvf6ORnX6YSAyeSudc/Hv1ih8/EDgTfO8DcA1caYWmPMCPA0cN9V29wHPOF5/Bxwm4iIF8YeV8bFMmpiVhIeEemrIeaMgrW3MmLCGNA+/pQ5Gt6hi0QWLVltO0rAm5+eTb0jh9jWg7ajBI13n/s27/7TR3GOjXl9394o+FlA4xWfN3m+Nu42xpgxoAeYP97OROQxESkTkbKOjo5phxka7GfIEcdg9o3T/t5QNC82nprIYlI69BdyKozLRXbvURriVmv/forak9dRMHiCsdER21GCQnT1r0nrOeGTCScB9xNrjHncGFNqjClNS0ub9vdHz4ul+H8fZNNHv+aDdHNT94INFIxW0X+p23aUgNfacJYMOhnN0fVzpiq84CZiZYjaE/tsRwl4oyPDFA6e5HzKOp/s3xsFvxnIueLzbM/Xxt1GRMKBRECv9gkQccU3Ey4uag5rH38yTcfcEwLStX8/ZZf7+BdO6s/XZGqP7yVGhgnP3+KT/Xuj4B8CikRksYhEAg8DO67aZgfwSc/jB4E3jTHGC2MrLyhYeyujJoz+s7quzmSkfi8XSSC3WG9pOFWpGYtocGQzr1XX1ZnMxVO7gN/+J+ltsy74np78F4BXgdPAs8aYChH5hojc69ns34H5IlIN/Anwvqmbyp6YuERqIpaQ3KHz8SeT3XOYuljt309XW/I68ge0jz+Zea0HOefIIjVjkU/275WfWmPMS8aYJcaYAmPMNz1f+5oxZofn8ZAx5iFjTKExZoMxptYb4yrvubhgPQUjlQz09diOErBa6itZSAejOv9+2sIWbyFeBqk7qWf5E3GOjZE/cJzWJN/07yEA37RVdsQWbSVCnNQcect2lIDVfMy95tCClXpB33TletbV6dL5+BOqqzhAvAwSttg3/XvQgq888tfdxphx0Fe5y3aUgGXq93KReHKXltqOEnTSMvNolEyim3VdnYl0nnT/Z5izxncL8mnBVwDEJSRTG1FI0nm9z+1EsnsOUx+7CkdYmO0oQak1eR35g8d9ckHRXBDVvJ9mSSc9u8BnY2jBV+/pSttAwcgZBvsv2Y4ScNrOVZFp2hnO1v79TDnytpDAAHUV2se/msvpJH+gnOZE3/XvQQu+ukJM0VYixUnNUW3rXK3x6OX+va5/P1M5nqmGl1sX6rfqTh0ikX5ksW9XCNCCr96Tv24bTiNcqtT5+FczdW/TTRx5y7R/P1Pp2QU0SQZR2sd/n44T7gX5ctb4Zv79ZVrw1XviE1OojSgksV3X1blalmf+vfbvZ6claR35A+W4nE7bUQJKVNM+miWdjEVFPh1HC776HV3zSykYPsPQYL/tKAGj7VwVWdq/9wrJ20Ii/dSd0ov8LnP374/5vH8PWvDVVaKX3EyUjOp8/Cto/957LrcsLrcwlP/696AFX11l8dptuIzQW/mW7SgBQ/v33pOxqIgWSdc+/hX81b8HLfjqKonJqdSG55PQplPnLtP+vXc1J65lcf8x7eN7+Kt/D1rw1Tg6U9dTMHya4aEB21Gs0/69D+RtIYk+Gs6U2U5inT/796AFX40jquBGomWUmmN628PL/fu0Fbr+vbdkrXa3Ls6f0Pn4/uzfgxZ8NY78dbfjMkLPab0Ay9S9TQ+xLC5ZbzvKnJGZV0wraUQ06h2w/Nm/By34ahyJ89OpC88jXvv4ZPUcpjZG+/fe1uTp4xuXy3YUq/zZvwct+GoCHfPXUzB0ipHhIdtRrNH+ve+YvC0k00tD5RHbUazxd/8etOCrCUQW3MQ8GaE2hPv47/Xvdf6912Wtcrcw2o+H7n1u/d2/By34agL569y/kBdPh+4ba9q/953MvGLamU9E417bUazxd/8etOCrCSSlZlDnyCOuNXTX1dH+ve+Iw0Fjwlpy+0K3j+/v/j1owVfXcD5lHQVDFYyODNuO4nfav/c9V+4NzKeHc1XHbUfxOxv9e9CCr64hovAmYmSYmvK3bUfxO+3f+16mp4/fVv665ST+Z6N/D1rw1TXkeW5YcfFU6M3H1/6972Xll3CeFMJDcD6+jf49aMFX15CyIIt6xyJiW0NvoavsnsPUxuj9a31JHA7OJawl99KRkOvjRzXtpcXP/XvQgq8m0T5/A4WDJ0NqXZ2WujPu+9fm+Pfldihy5d5IKt2cqzxqO4rfjI2OUDBwjP/NOGAAABetSURBVKYk/7961IKvrimy6BZiZJjqEFofv+nIywAsXH2n5SRzX/a67QC0HnvFchL/qT2xjwQGcBTe7PexteCrayrYsN19n9tToXPDirD63XSQzKLiNbajzHmZecXu+9w2vmM7it9cOP4aAItLt/t97FkVfBFJEZHXRaTK82fyBNs5ReSY52PHbMZU/pWQNJ/qiGKS2kLjjTWX08niS4epT1yPOPR8yB+aUzZS2H+UsdER21H8Iq51LzVhi5mfnu33sWf7E/1V4A1jTBHwhufz8QwaY1Z7Pu6d5ZjKzy6kb6ZwtJJLPRdsR/G5ulOHSKEXFm+1HSVkhBfcQrwMUh0C03+HBvooGqqgI3WTlfFnW/DvA57wPH4CuH+W+1MBKKHkdsLFRc2hV21H8bmOcncveZGFl9uhKn/9XbiMcPHEa7aj+FxV2RtEySjzltq5v8JsC366MabV87gNSJ9gu2gRKRORAyJyzf8UROQxz7ZlHR0ds4ynvKFw3S0MmkiGKuf+Qlfzmt7hnCOL9OwC21FCRnLaQvdtNVvn/ro6fad3MmrCKCz17/z7yyYt+CKyU0ROjvNx35XbGWMMYCbYTa4xphR4FPiuiEz422SMedwYU2qMKU1LS5vOsSgfiYqOoWreSjK65va6OiPDQxQNHqc1ZaPtKCGnM20TRcOnGejrsR3Fp1I79lMVuYzY+CQr409a8I0x24wxK8b5eAFoF5GFAJ4/z0+wj2bPn7XAW4BOfwgyA5k3kOc6R2dLg+0oPlN99C1iZJiIolttRwk5MUtvI1LGqC6bu7PBerraKRitpmehvfWZZtvS2QF80vP4k8ALV28gIskiEuV5nArcAJya5bjKz1JXueek15e9bDmJ7/RUvI7TCAXr77IdJeQUlm5jxIQzcGbutg1ry17BIYbk5XbaOTD7gv93wO0iUgVs83yOiJSKyI892ywDykSkHNgF/J0xRgt+kMlfsZlu4jC1b9mO4jNJbfuoiSgiMUVbif4WE5dIVdQyUjvm7m01R86+Sb+JpmCNvRlg4bP5ZmNMF/C+t5uNMWXAH3ge7wNWzmYcZZ8jLIzauLXkdB/CuFxzbo76pZ4LFI2c4VDWx21HCVm9C29gY/2PuNjRSnLaQttxvC7zwrtUx6xiVWSUtQxz67dW+dRo7lYy6KSp5oTtKF5XU/Ya4eIivkSXQ7YleeUdOMRQe2juLbPQ1lhNjmlh0PL6TFrw1ZRlrXH3tluOzr35+EOVbzJkIihcZ2d+tILCVTdyycxjrGbuLcd9zvPeV/qqO6zm0IKvpiwrv4RW0ohomHs3Nk/vPEBV9Aqi58XajhKywiMiqY5dQ9aFuTf911H3Fl0kkrfM7v0VtOCrKROHg8bkjRT2H55T656cb65jsauBvixdDtm2kUU3kW3aaK6tsB3Fa1xOJ/m971KXYH99Ji34alrCi28ngQGqjsydl90NB93r+aWv/aDlJCqr9B4Amg69aDmJ99Sc2Oden6nQ/vtDWvDVtBRs/CBjxkH38ZdsR/GasNqdnCdFb2cYALILV9AkGUTXv2k7itd0Hv01AIs33mM5iRZ8NU2JyamcjSwhrW1urGw4NjpCYV8Z9UmbrL/cVm7N82+gaOAYQ4P9tqN4RVLLHqrCi6wsh3w1/QlX09abtZVCZw2dbedsR5m16iNvkcAAYUvszp5QvxVdcgcxMkzVoeBfZqHnQgdLRk7TmREY7w9pwVfTlrrmAwDUHQj+e9lcPP4SY8ZB4Wb7L7eVW9GG7QybCPorgn8Zj+oDvyZMDMnX3W07CqAFX81A/opNdJKEoyb41z1JbXubqsilJCan2o6iPGLiEjkbvZKMjuC/7aHz7Gv0EkuhxeUUrqQFX02bIyyMusRNFFx6F+fYmO04M9bZ1kiRs5rurMD4ZVS/1b/oFvJcjbSdq7IdZcaMy0Ve9wGq4tYTHhFpOw6gBV/NkCzZRhJ9VB3bbTvKjNUddE/9S139ActJ1NUWrnNPkb08ZTYY1Z06xAIu4CwInKu3teCrGSnceA9OI1wsD97pmVK9ky4SKVhpb31yNb5FS1bTShqRdcHbNmw/4p6Omb/xvkm29B8t+GpGklIzqI4oZn5rcC6z4Bwbo+DSu9QmbsQRFmY7jrqKOBycm389S/oPMzI8ZDvOjCQ07aImbDGpmbm2o7xHC76asQvZt7Bk7CwdLfW2o0xbZdlOkrmEY8mdtqOoCUSV3E2sDFF5IPheRfZ0tVM8XMH5jMB6f0gLvpqxjPUfAqB27y8sJ5m+3mM7GDFhLNnygO0oagJLN3+QARPFwIngW2bh7Du/IFxczF/3IdtRfocWfDVjecvW0yLpRNcG1/rlxuUiq30XZ+atJj4xxXYcNYHomDgqY0vJ69yNcblsx5mWsLMv00EyhasC44Kry7TgqxkTh4NzaTezdOAo/Ze6bceZsnNnj7lvRrFY2zmBbrRoO+l0UXNin+0oUzY02M/SvoPUzr8p4N4f0oKvZiV+1X1EySiVe5+3HWXKWg66W1B5NzxoOYmaTOEND+A0QkfZr2xHmbLKAy8RI8NELw+81Ve14KtZKd5wO93E4TwdPG+sJTe+QVVYIenZBbajqEmkLMjibGQJC1qCZ3rm0MkXGTBRFG8OvOs7tOCrWQmPiKQq8XqKevYGxU1ROtsaWTJ6hs5s+2uTq6npyb2dAmcdLfWVtqNMyuV0kt+1hzNxGwPy7mla8NWshS29myT6qAyC1Q1r9z6HQwwLSgNr9oSaWNYmd+vt3P7nLCeZXHX526RxEeeS7bajjEsLvpq1JTfcz4gJ51J54F8GH1nzKq2kkb98g+0oaopyClfS4Mgmrv4121Em1XX4ecaMg6IbAnO6rxZ8NWtxCcmcnreGnPNvBvT0uf5L3SztL6Mh7Wa92UmQaUm/leKhE/R0tduOck0LW9+gMmo5SakZtqOMS3/qlVeMLLmHLNMe0NPnzux5jmgZJWGdzs4JNqkbHiJCnFTuecZ2lAk1nD5MnuscffmB92btZVrwlVcs2fowoyaMjgOB+wspp56ng2SWrr/ddhQ1TYWrtrgv8qsM3LZhy/6ncRmh4KZHbUeZ0KwKvog8JCIVIuISkdJrbHeXiFSKSLWIfHU2Y6rAlDg/nVPz1pLb9kpAtnX6ei9S0neAmrRtAXcxjJqcOBw0ZNzJssEjdHe22Y7zPsblIrPpZU5HrQioxdKuNtsz/JPAA8CESyaKSBjwA2A7UAI8IiIlsxxXBaDh4vvINOepOhZ4Nzg/s/tZomWUpNKP2I6iZiht0+8RIU7O7n7KdpT3qT9zmFxXI30FgX2rzFkVfGPMaWPMZJNjNwDVxphaY8wI8DQQOAtEK68p3vowIyaMC+8GXlsn7PTznCeFJaWBczMKNT0FK6+nSTKYdzbw2jrt+57CaYSCrY/YjnJN/ujhZwGNV3ze5PnauETkMREpE5Gyjo4On4dT3pOYksbpmFLy2l7D5XTajvOe3u4uSvoPUbtA2znBTBwOGhfeybKhY3S1N9mO8x7jcpHV/DJnolaSmrHIdpxrmrTgi8hOETk5zodPztKNMY8bY0qNMaVpaWm+GEL50GjJh8mgg9MHX7Ud5T1n3vgZUTJKyqaP2Y6iZiljy8cJFxdVbz5hO8p7qo7tIce00F8cmHPvrzRpwTfGbDPGrBjn44UpjtEM5Fzxebbna2oOWn7ro/SbaPrf/U/bUd4Td+Y5GhzZFK0OrKVq1fQtLllPdVgB86t/aTvKey7ue4JhE8HS2z5hO8qk/NHSOQQUichiEYkEHgYCrwmnvGJebDynkm+h5OIuBvsv2Y5Dc+1pSkZP0rroPr3Yao7oLPgQRc5qGk4fth2FkeEhlnS+zsmELSQkzbcdZ1KznZb5IRFpAjYDvxGRVz1fzxSRlwCMMWPAF4BXgdPAs8aYitnFVoFs3vqPEieDVOyyP5vi3Fs/BSDv1t+3nER5S+Gtn2LMOGh5+z9sR6Fi93Mkc4nwNYE79/5Ks52l8ytjTLYxJsoYk26MudPz9RZjzN1XbPeSMWaJMabAGPPN2YZWga1k0920kUrkyWet5jAuFzmNO6iIXEXGoiKrWZT3pGbkUBGznvyW3+AcG7OaxZQ/TReJLL/xfqs5pkpf4yqvc4SFUZd1D8sHy2hrrLaW49SBV8g2rfQve8haBuUbYysfIZ0uKt62d+OdrvYmVvTtoyp9O+ERkdZyTIcWfOUTuds+iwB1r/2rtQyD+39MLzGsvONT1jIo31h52yNcIAHnoZ9Yy3D21R8RKU4W3vo5axmmSwu+8onMxUs5Ma+UgsZfWrkxyoXzzVzX+xan0j7AvNh4v4+vfCsyKprKzPtZ2b+f9qYav4/vcjrJrXuGisjryC1e7ffxZ0oLvvIZs+7TLOACJ3b5v5cfjGdfanoWbfs84eKi9rUf+n3sk28/T6ZpZ3BV4E/FvJIWfOUzK25+kHbmE3bEvy+7XU4n2bXPcCpyJbnL1vl1bOU/WfnLOB5dSsG55/z+KtL57r9zgQRW3vZRv447W1rwlc+ER0RSm/sQ1w0dpuHMEb+Ne/yt/ybbtDFwXXCdfanpc679fRZwgfLX/XehX3Ptaa7r30flwvuJio7x27jeoAVf+dTSD36ZQRNJ+6v/129jRh78Z9pIY9Udn/TbmMqO6259mEbJJOHIv/ptWe6ml/4BJw4K7/mKX8bzJi34yqeS0xZyPO2DrL7wKp0tDT4fr7LsTUpGTlC/5JNEREb5fDxlV1h4OC0ln6ForIpT+1/2+XjdnW2s7Pg15cl3kJaZ5/PxvE0LvvK57Lv/lDCcVP3a92f5/bu+Qy+xrLzniz4fSwWGVR/4LBdIYOyd7/p8rNMvfocYGSbtzj/1+Vi+oAVf+VxW/nLK429kectz9Fzw3ZLXDZXHWN33NhWZDxIbn+SzcVRgiY6JozL3UVYNvkvNiQM+G6f/UjfFDU9SPm8jecsmvMFfQNOCr/wi8c6/IIEBTj33Nz4bo+vFv2SQKJbc9+c+G0MFppL7/4weYul76Ws+G+P4c39LCr1E3xa8d2nVgq/8omDlJsrib2NV89N0tp3z+v6rjr3N2r49HF/0MeanZ3t9/yqwJSancir/M6waPOiTezF0d7axov4JjsbcQHHprV7fv79owVd+k3HfN4hgjJrnvu71fQ++8nUuEs+KB//C6/tWwWH1h/+cDpJh5195fcbOmee+QSxDJN/zDa/u19+04Cu/yS5cwZHUe1jb8QJ1pw55bb/lbz7NdUOHqSz6H8Qnpnhtvyq4zIuNp7bk8ywbPcWRV7x3R6zG6hOsaX2Ww0l3BG3v/jIt+Mqvljz8d/RJDMO/+pJX7nvbf6mb9D3/m3pHDmsf/H+8kFAFs3Uf+jLVYQXkvvtX9FzsnPX+jMtF77N/yLBEsPj3/sELCe3Sgq/8KjltIdWr/xdLR09x6BffnvX+Tvz8q2TQwdCd3yYyKtoLCVUwC4+IxNzzTySbHs78fPYXRpXt+BeWj5RzevlXSM3M9UJCu7TgK78rvfdznIxaTUnFP9JUfXLG+zl14BXWtz3Nwfn3s3TjHV5MqIJZ0eobOZTxMBu7nufE7pnf+7a1oZKiY3/L6YgS1j/wx15MaI8WfOV34nCQ8sjjOCWM0Scfpf9S97T3cb65jvRXHqPFsZBlH5/9KwU1t1z38W9R58glZ9cXaak7M+3vHxroo/9njxBmnMR95Ic4wsJ8kNL/tOArKzLzimm89Z9Z5DzHmR99clr9/KHBfi7+9PeINsO4PvLzoLh5tPKvmLhEIh59EgeGwZ8/wkBfz5S/17hcnPjRZyh01lBz43fIKVrlw6T+pQVfWbPypg9xqOCLrOt7i0P/8ukpFf2hwX4qv3c/xWOVVG7+li5/rCaUXbiCupu+S95YHbXfv3dKRd+4XBz80edY3/MK+xc9xuptj/ghqf9owVdWbfzYX7N/4SfY2PU85d++95ozK9oaq6n/x9tYNfguB5d/jbV3fcp/QVVQWnXrRziy9v9j2VA5zd+5lZb6ygm37eu9yOHvPMim9qc5mPYgmz71LT8m9Q8xxtjOMKHS0lJTVlZmO4byMeNycfDpb1Ja+W0uSBJ1y/+Qkjs+/d6c+q72Js6+8q8sr/sJ4cbJmc1/r8VeTcuxN56mcM+XEQzH8z5F0fY/JDVjEeCe2nvq9SfIOf590kwn7+b/IZs+/jeIIzjPh0XksDFm3AsGtOCrgHH2yG546U9ZMnaWURNGu2MBDlxkuM7jEEP5vA2kPvRdsvKX246qglBrQyVtz3yZNQP7cBmhXVIZkwjSXe1EipPqsALG7vwWSzfcbjvqrGjBV0HDuFxUlr3BxfLfENlbj8HBaEoRGRseYPHyjbbjqTmg4cwRWg4+R0RXJeIaYyQhl8SV21m28c6gPau/khZ8pZQKEdcq+MH/35lSSqkpmVXBF5GHRKRCRFwiMuGqQiJSLyInROSYiOgpu1JKWRA+y+8/CTwA/GgK295ijJn9akZKKaVmZFYF3xhzGkBEvJNGKaWUz/irh2+A10TksIg8dq0NReQxESkTkbKODt/d/1QppULNpGf4IrITyBjnqb8wxrwwxXG2GGOaRWQB8LqInDHG7BlvQ2PM48Dj4J6lM8X9K6WUmsSkBd8Ys222gxhjmj1/nheRXwEbgHELvlJKKd/weUtHRGJFJP7yY+AO3G/2KqWU8qNZXXglIh8Cvg+kAd3AMWPMnSKSCfzYGHO3iOQDv/J8SzjwpDHmm1PcfwfQMMN4qUCozQrSY577Qu14QY95unKNMWnjPRHQV9rOhoiUTXS12Vylxzz3hdrxgh6zN+mVtkopFSK04CulVIiYywX/cdsBLNBjnvtC7XhBj9lr5mwPXyml1O+ay2f4SimlrqAFXymlQkTQF3wRuUtEKkWkWkS+Os7zUSLyjOf5gyKS5/+U3jOF4/0TETklIsdF5A0RybWR05smO+YrtvuwiJhrLdUdLKZyzCLyEc+/dYWIPOnvjN42hZ/tRSKyS0SOen6+77aR01tE5Ccicl5Exr0QVdy+5/n7OC4ia2c9qDEmaD+AMKAGyAcigXKg5KptPg/80PP4YeAZ27l9fLy3ADGex58L5uOd6jF7tovHvVzHAaDUdm4//DsXAUeBZM/nC2zn9sMxPw58zvO4BKi3nXuWx3wTsBY4OcHzdwMvAwJsAg7OdsxgP8PfAFQbY2qNMSPA08B9V21zH/CE5/FzwG0SvOs5T3q8xphdxpgBz6cHgGw/Z/S2qfwbA/wN8C1gyJ/hfGQqx/w/gB8YYy6Ce50qP2f0tqkcswESPI8TgRY/5vM6415A8sI1NrkP+JlxOwAkicjC2YwZ7AU/C2i84vMmz9fG3cYYMwb0APP9ks77pnK8V/oM7jOEYDbpMXte6uYYY37jz2A+NJV/5yXAEhHZKyIHROQuv6Xzjakc818BHxORJuAl4Iv+iWbNdH/fJzXbO16pACUiHwNKga22s/iSiDiAbwOfshzF38Jxt3Vuxv0qbo+IrDTGdFtN5VuPAP9hjPlHEdkM/KeIrDDGuGwHCxbBfobfDORc8Xm252vjbiMi4bhfCnb5JZ33TeV4EZFtwF8A9xpjhv2UzVcmO+Z4YAXwlojU4+517gjyN26n8u/cBOwwxowaY+qAs7j/AwhWUznmzwDPAhhj9gPRuBcZm6um9Ps+HcFe8A8BRSKyWEQicb8pu+OqbXYAn/Q8fhB403jeEQlCkx6viKzBfY/he+dAXxcmOWZjTI8xJtUYk2eMycP9vsW9xpgyO3G9Yio/18/jPrtHRFJxt3hq/RnSy6ZyzOeA2wBEZBnugj+Xb4u3A/iEZ7bOJqDHGNM6mx0GdUvHGDMmIl8AXsX9Lv9PjDEVIvINoMwYswP4d9wv/apxv0HysL3EszPF4/0HIA74b8970+eMMfdaCz1LUzzmOWWKx/wqcIeInAKcwJ8ZY4L1letUj/krwL+JyB/jfgP3U0F88oaIPIX7P+1Uz/sSXwciAIwxP8T9PsXdQDUwAPz+rMcM4r8vpZRS0xDsLR2llFJTpAVfKaVChBZ8pZQKEVrwlVIqRGjBV0qpEKEFXymlQoQWfKWUChH/PzPtfkR2CDe5AAAAAElFTkSuQmCC\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "deletable": false,
        "editable": false,
        "nbgrader": {
          "cell_type": "markdown",
          "checksum": "63d19761c024ae3c603e5820ffe793ff",
          "grade": false,
          "grade_id": "cell-d0a5a2108321c342",
          "locked": true,
          "schema_version": 3,
          "solution": false,
          "task": false
        },
        "id": "iuzbZ1_t5zsN"
      },
      "source": [
        "# Perturbation\n",
        "\n",
        "Consider now the modified potential: add to the square well potential the additional term \n",
        "\n",
        "$$\n",
        "V(x) = -\\frac{\\hbar^2}{2m}\\, \\gamma\\, x(x-a)\n",
        "$$\n",
        "\n",
        "for $0 < x < a$, where $\\gamma$ is a constant.\n",
        "\n",
        "An analytic solution is no longer possible, but the numeric solution is a straightforward extension of what we did in the previous section."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "deletable": false,
        "editable": false,
        "nbgrader": {
          "cell_type": "markdown",
          "checksum": "45ffb8bcf1de11742dcb4f007d953876",
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          "grade_id": "cell-65d49ff5520f5952",
          "locked": true,
          "schema_version": 3,
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        },
        "id": "PB7dN-Va5zsN"
      },
      "source": [
        "## Numeric solution\n",
        "\n",
        "Again, define a grid function $\\psi_j$. The Schroedinger equation then becomes\n",
        "\n",
        "$$\n",
        "-\\left( \\psi_{j-1} + \\psi_{j+1} - 2\\psi_{j} \\right) - \\gamma h^2 x_j (x_j - a) \\psi_j = k^2 h^2 \\psi_j \\; , \\qquad j = 1, \\cdots, N-1\n",
        "$$\n",
        "\n",
        "so that the diagonal elements of the Hamiltonian matrix are no longer constants.\n",
        "\n",
        "Construct the hamiltonian matrix, solve for the eigenvalues and plot the ground state wave functions for a range of $\\gamma$. Discuss the structure of the wave function for $\\gamma > 500$."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "deletable": false,
        "nbgrader": {
          "cell_type": "code",
          "checksum": "a5f51202140acfac61f1320fcbdaff4b",
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          "grade_id": "cell-f7dc2f611e4b19af",
          "locked": false,
          "schema_version": 3,
          "solution": true,
          "task": false
        },
        "id": "ULy7lmMJ5zsN"
      },
      "source": [
        "def hamiltonian_perturbed(gamma, npts):\n",
        "    \"\"\"Construct the eigenvalue matrix for the discretized 1D Schroedinger equation.\n",
        "    \n",
        "    Parameters\n",
        "    ----------\n",
        "    gamma : float\n",
        "        The extra potential is $gamma * x * (x-1)$\n",
        "    npts : int\n",
        "        The number of nodes in the mesh: $x_j = a*j /npts$, with $j=0, ..., npts$\n",
        "        \n",
        "    Returns\n",
        "    -------\n",
        "    ham : ndarray, shape(npts-1, npts-1)\n",
        "        The matrix of the mesh version of the Sturm-Liouville operator.\n",
        "    \"\"\"\n",
        "    x = np.arange(npts - 1) / (npts - 2)\n",
        "    h = 1 / (npts - 2)\n",
        "    matr = np.zeros((npts - 1, npts - 1))\n",
        "    np.fill_diagonal(matr[1:, :], -1)\n",
        "    np.fill_diagonal(matr[:, 1:], -1)\n",
        "    np.fill_diagonal(matr, 2 - gamma * h**2 * x * (x - 1))\n",
        "    return matr"
      ],
      "execution_count": 12,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "deletable": false,
        "editable": false,
        "nbgrader": {
          "cell_type": "code",
          "checksum": "32bbafba7b50af91a34974157e408c1d",
          "grade": true,
          "grade_id": "cell-ad4764121a24f8dc",
          "locked": true,
          "points": 4,
          "schema_version": 3,
          "solution": false,
          "task": false
        },
        "id": "ADEtm_Bq5zsP"
      },
      "source": [
        "gamma, N = 590, 11\n",
        "h = hamiltonian_perturbed(gamma, N)\n",
        "\n",
        "assert h.shape == (N-1, N-1)\n"
      ],
      "execution_count": 13,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "deletable": false,
        "nbgrader": {
          "cell_type": "code",
          "checksum": "07f88c901c4a91b916c64cf201d272ec",
          "grade": false,
          "grade_id": "cell-c6b6aa782bac0d62",
          "locked": false,
          "schema_version": 3,
          "solution": true,
          "task": false
        },
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 265
        },
        "id": "gltl3iUx5zsP",
        "outputId": "3fbf4c2e-b63b-4513-d318-0afe7685c629"
      },
      "source": [
        "gamma, N = 400, 100\n",
        "h = hamiltonian_perturbed(gamma, N)\n",
        "\n",
        "_, vecs = np.linalg.eigh(h)\n",
        "plt.plot(np.arange(N + 1) / N, [0] + list(vecs[:, 0]) + [0])\n",
        "plt.show()"
      ],
      "execution_count": 14,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "deletable": false,
        "editable": false,
        "nbgrader": {
          "cell_type": "markdown",
          "checksum": "4d52ce55d39ae5ebdc4660dd09184de3",
          "grade": false,
          "grade_id": "cell-3cfcd31b5b76539e",
          "locked": true,
          "schema_version": 3,
          "solution": false,
          "task": false
        },
        "id": "-RPoNd6g5zsQ"
      },
      "source": [
        "Bonus: discuss the structure of the spectrum at large $\\gamma$."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "ere0h9bM5zsQ"
      },
      "source": [
        ""
      ],
      "execution_count": 14,
      "outputs": []
    }
  ]
}