{
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   "source": [
    "# Week II - Numerical solution of the 1D Schrödinger equation: the Numerov's method"
   ]
  },
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   "source": [
    "For the full lecture on this topic, check out yesterday's lecture by Prof. Peressi on *The Numerov’s method for the 1D Schrödinger equation* (slides on Moodle) and Prof. Giannozzi lecture notes here https://www.fisica.uniud.it/~giannozz/Corsi/MQ/LectureNotes/mq.pdf (from which the following tutorial is inspired).\n",
    "\n",
    "\n",
    "## Numerov’s method and the Schrödinger equation\n",
    "\n",
    "\n",
    "As you have seen in the lecture of yesterday, the Numerov's method is useful to integrate second-order differential equations of the general form\n",
    "\n",
    "$$\\frac{d^2y}{dx^2} = g(x)y(x) + s(x).$$\n",
    "\n",
    "The Schrödinger equation \n",
    "$$\\frac{\\hbar^2}{2m}\\frac{d^2\\psi}{dx^2} + V(x)\\psi(x)  = E\\psi(x)$$\n",
    "falls indeed in this class\n",
    "\n",
    "$g(x) = -\\frac{2m}{\\hbar^2}(E − V(x))$ and $s(x) = 0$\n",
    "\n",
    "and can be solved by adopting the Numerov's approach.\n",
    "\n",
    "### The algorithm\n",
    "Let us take a one-dimensional (1D) finite box and divide it into $N$ small intervals of equal width $\\Delta x$, hence defying a grid $x_i$ with $y_i=y(x_i)$.\n",
    "\n",
    "The **Numerov's formula** allows obtaining $y_{n+1}$ starting from $y_n$ and $y_{n−1}$ and, recursively, the values of function over the entire box:\n",
    "\n",
    "$$\n",
    "y_{n+1} \\left(1 + g_{n+1}\\frac{(\\Delta x)^2}{12}\\right)=2y_{n}\\left[1-5g_{n-1}\\frac{(\\Delta x)^2}{12}\\right] - y_{n-1} \\left[1+g_n\\frac{(\\Delta x)^2}{12}\\right]+\\left[s_{n+1} + 10s_n + s_{n-1}\\right]\\frac{(\\Delta x)^2}{12}+ \\mathcal{O}[(\\Delta x)^6]\n",
    "$$\n",
    "where $g_n=g(x_n)$ and $s_n = s(x_n)$.\n",
    "\n",
    "For the Schödinger equation we can write a more compact expression:\n",
    "$$\n",
    "y_{n+1}  = \\frac{(12-10f_n)y_n-f_{n-1}y_{n-1}}{f_{n+1}}\n",
    "$$\n",
    "where $ f_n= 1 + g_n (\\Delta x)^2 /12 $ and $g_n = 2m/\\hbar^2(E-V(x_n))$.\n",
    "\n",
    "> Note: the values of the function $y$ calculated at the first two points are needed to solve the equation (different from usual boundary conditions for second-order differential equations).\n"
   ]
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    "### The shooting method\n",
    "\n",
    "The *shooting method* is very similar to the bisection procedure to identify the zero of a given function. We start by specifying an initial energy range $[E_{min},E_{max}]$ that must contain the unknown eigenvalue $E$. At the beginning, a tentative guess for E is set at $(E_{min}+E_{max})/2$. Then, the function is integrated starting from $x = 0$ and going towards positive values of $x$; during the process, the number of nodes  is counted by monitoring the changes of sign of the function. If the number of nodes is larger than the target one $n$, it means $E$ is too high. On the contrary, if the number of nodes is smaller than $n$, $E$ is too low. At each iteration, we set the lower half-interval $[E_{min},E_{max}=E]$, or the upper half-interval $[E_{min}=E,E_{max}]$, respectively; A new trial eigenvalue $E$ in the mid-point of the new interval, iterate the procedure. When the energy interval is smaller than a pre-determined threshold, we assume that convergence has been reached.\n",
    "\n",
    "### 1D harmonic oscillator\n",
    "In the following, we will see a Python implementation to solve the Schrödinger equation for the quantum harmonic oscillator. We will use the Numerov’s algorithm for integration, while eigenvalues of a pre-determined number n of nodes will be identified using the shooting method. For simplicity, dimensional units will be adopted. \n",
    "\n",
    ">The parity of the function determines the choice of the starting points for the recursion. For $n$ odd, the two first points can be chosen as $y_0 = 0$ and an arbitrary finite value for $y_1$. For $n$ even, $y_0$ is arbitrary and finite, $y_1$ is determined by Numerov’s formula by setting $f_1 = f_{-1}$ and $y_1 = y_{−1}$:\n",
    "> $$y_1 = \\frac{(12 − 10f_0)y_0}{2f_1}$$"
   ]
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   "source": [
    "# Loading Numpy module\n",
    "import numpy as np\n",
    "\n",
    "# Here we code our solver\n",
    "def integrate_1D_harm_numerov(x_max,n_points,n_nodes,filename='res.txt'):\n",
    "    '''\n",
    "    This functions solves the one-dimensional Schroedinger equation\n",
    "    for the harmonic oscillator by using the Numerov's method\n",
    "    '''\n",
    "    x = np.linspace(0,x_max, n_points+1,endpoint=True)\n",
    "    dx =  float(x_max)/n_points \n",
    "    ddx12 = dx**2/12.0\n",
    "    f = np.zeros(n_points+1,dtype=np.float64)\n",
    "    y = np.zeros(n_points+1,dtype=np.float64)\n",
    "    # Here below we define the potential for an harmonic oscillator\n",
    "    v_pot = map(lambda xx: 0.5*xx**2, x)\n",
    "    v_pot = np.array(list(v_pot),dtype=np.float64)\n",
    "\n",
    "    #\n",
    "    def solve_numerov(e):\n",
    "        '''\n",
    "        This function implements the Numerov's algorithm\n",
    "        for a given input energy e\n",
    "        '''\n",
    "        f[0]=ddx12*(2.0*(v_pot[0]-e))\n",
    "        cs_index=-1\n",
    "        for i in range(1,n_points+1):\n",
    "            f[i]=ddx12*2.0*(v_pot[i]-e)\n",
    "            #\n",
    "            #if f(i) is exactly zero the change of sign is not observed\n",
    "            # the following line prevents missing a change of sign  \n",
    "            if f[i] == 0.0:\n",
    "                f[i]=1e-20\n",
    "\n",
    "            if f[i]*f[i-1]<0:\n",
    "                cs_index = i\n",
    "                !\n",
    "        if cs_index < 0: \n",
    "            print('WARNING: no classical turning point found.')\n",
    "\n",
    "        # f = 1+g_n(dx^2/12) with g_n = (2.0*(e-v_pot[0]), but we used e-v and without the + 1\n",
    "        f[:] = 1.0 - f[:]\n",
    "        y[:] = 0.0\n",
    "\n",
    "        # number of nodes in the semi-axis x>0\n",
    "        h_n_nodes = int(n_nodes)//2\n",
    "\n",
    "        if (2*h_n_nodes == n_nodes):\n",
    "           # even number of nodes: wavefunction is even\n",
    "           y[0] = 1.0\n",
    "           # assume f(-1) = f(1)\n",
    "           y[1] = 0.5*(12.0-10.0*f[0])*y[0]/f[1]\n",
    "        else:\n",
    "           # odd number of nodes: wavefunction is odd\n",
    "           y[0] = 0.0\n",
    "           y[1] = dx\n",
    "        #\n",
    "        # outward integration and count number of crossings\n",
    "        #\n",
    "        n_cross = 0\n",
    "        for j in range(1,n_points):\n",
    "            y[j+1]=((12.0-10.0*f[j])*y[j]-f[j-1]*y[j-1])/f[j+1]\n",
    "            if y[j]*y[j+1]<0:\n",
    "               n_cross+=1\n",
    "        return n_cross, h_n_nodes,y\n",
    "    \n",
    "    # Here we initialize the bisection method\n",
    "    e_up = np.max(v_pot)\n",
    "    e_lw = np.min(v_pot)\n",
    "    e_iter = 0\n",
    "    data = []\n",
    "\n",
    "    # Bisection loop\n",
    "    while (np.abs(e_up-e_lw)>1e-10 and e_iter<1e6):\n",
    "        e = 0.5 * (e_up+e_lw)\n",
    "        n_cross,h_n_nodes,y = solve_numerov(e)\n",
    "        if (n_cross > h_n_nodes):\n",
    "            e_up = e\n",
    "        else:\n",
    "            e_lw = e\n",
    "        #\n",
    "        data.append([e_iter,n_cross,h_n_nodes,e])\n",
    "        print('Iteration = {}, number of crossing = {} and nodes = {} for pos axis, energy = {}'.format(e_iter,n_cross,h_n_nodes,e))\n",
    "        e_iter+=1\n",
    "    \n",
    "    # Writing to text file\n",
    "    to_write = []\n",
    "    for ii in range(n_points,0,-1):\n",
    "        to_write.append([-x[ii], (-1)**n_nodes*y[ii],y[ii]**2])\n",
    "    for ii in range(n_points+1):\n",
    "        to_write.append([x[ii], y[ii],y[ii]**2])\n",
    "\n",
    "    np.savetxt(filename,to_write)\n",
    "\n",
    "    return data,y\n"
   ]
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   "source": [
    "-------------\n",
    "\n",
    "### Numerical experiments \n",
    "\n",
    "Now let's run the code and visualize the results.\n",
    "We start with the simple case of a nodeless wavefunction (ground state).\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "fa938e53",
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   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Iteration = 0, number of crossing = 3 and nodes = 0 for pos axis, energy = 6.25\n",
      "Iteration = 1, number of crossing = 2 and nodes = 0 for pos axis, energy = 3.125\n",
      "Iteration = 2, number of crossing = 1 and nodes = 0 for pos axis, energy = 1.5625\n",
      "Iteration = 3, number of crossing = 1 and nodes = 0 for pos axis, energy = 0.78125\n",
      "Iteration = 4, number of crossing = 0 and nodes = 0 for pos axis, energy = 0.390625\n",
      "Iteration = 5, number of crossing = 1 and nodes = 0 for pos axis, energy = 0.5859375\n",
      "Iteration = 6, number of crossing = 0 and nodes = 0 for pos axis, energy = 0.48828125\n",
      "Iteration = 7, number of crossing = 1 and nodes = 0 for pos axis, energy = 0.537109375\n",
      "Iteration = 8, number of crossing = 1 and nodes = 0 for pos axis, energy = 0.5126953125\n",
      "Iteration = 9, number of crossing = 1 and nodes = 0 for pos axis, energy = 0.50048828125\n",
      "Iteration = 10, number of crossing = 0 and nodes = 0 for pos axis, energy = 0.494384765625\n",
      "Iteration = 11, number of crossing = 0 and nodes = 0 for pos axis, energy = 0.4974365234375\n",
      "Iteration = 12, number of crossing = 0 and nodes = 0 for pos axis, energy = 0.49896240234375\n",
      "Iteration = 13, number of crossing = 0 and nodes = 0 for pos axis, energy = 0.499725341796875\n",
      "Iteration = 14, number of crossing = 1 and nodes = 0 for pos axis, energy = 0.5001068115234375\n",
      "Iteration = 15, number of crossing = 0 and nodes = 0 for pos axis, energy = 0.49991607666015625\n",
      "Iteration = 16, number of crossing = 1 and nodes = 0 for pos axis, energy = 0.5000114440917969\n",
      "Iteration = 17, number of crossing = 0 and nodes = 0 for pos axis, energy = 0.49996376037597656\n",
      "Iteration = 18, number of crossing = 0 and nodes = 0 for pos axis, energy = 0.4999876022338867\n",
      "Iteration = 19, number of crossing = 0 and nodes = 0 for pos axis, energy = 0.4999995231628418\n",
      "Iteration = 20, number of crossing = 1 and nodes = 0 for pos axis, energy = 0.5000054836273193\n",
      "Iteration = 21, number of crossing = 1 and nodes = 0 for pos axis, energy = 0.5000025033950806\n",
      "Iteration = 22, number of crossing = 1 and nodes = 0 for pos axis, energy = 0.5000010132789612\n",
      "Iteration = 23, number of crossing = 1 and nodes = 0 for pos axis, energy = 0.5000002682209015\n",
      "Iteration = 24, number of crossing = 0 and nodes = 0 for pos axis, energy = 0.49999989569187164\n",
      "Iteration = 25, number of crossing = 1 and nodes = 0 for pos axis, energy = 0.5000000819563866\n",
      "Iteration = 26, number of crossing = 1 and nodes = 0 for pos axis, energy = 0.4999999888241291\n",
      "Iteration = 27, number of crossing = 0 and nodes = 0 for pos axis, energy = 0.4999999422580004\n",
      "Iteration = 28, number of crossing = 0 and nodes = 0 for pos axis, energy = 0.49999996554106474\n",
      "Iteration = 29, number of crossing = 1 and nodes = 0 for pos axis, energy = 0.4999999771825969\n",
      "Iteration = 30, number of crossing = 0 and nodes = 0 for pos axis, energy = 0.49999997136183083\n",
      "Iteration = 31, number of crossing = 0 and nodes = 0 for pos axis, energy = 0.4999999742722139\n",
      "Iteration = 32, number of crossing = 1 and nodes = 0 for pos axis, energy = 0.4999999757274054\n",
      "Iteration = 33, number of crossing = 0 and nodes = 0 for pos axis, energy = 0.49999997499980964\n",
      "Iteration = 34, number of crossing = 0 and nodes = 0 for pos axis, energy = 0.4999999753636075\n",
      "Iteration = 35, number of crossing = 0 and nodes = 0 for pos axis, energy = 0.49999997554550646\n",
      "Iteration = 36, number of crossing = 0 and nodes = 0 for pos axis, energy = 0.49999997563645593\n"
     ]
    }
   ],
   "source": [
    "# x_max = 5, 1000+1 points, 0 nodes\n",
    "_ = integrate_1D_harm_numerov(5,100,0,'zero_nodes.dat')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5683463d",
   "metadata": {},
   "source": [
    "In a few iterations we have found the correct ground state total energy (i.e. $0.5$) and the right number of crossings, let's look at the wavefunction $\\psi(x)$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "aca73c0a",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x10e54b550>"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
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ZdvPqamnbtuiMJ1TtvQ9a0AH7odgBEBWx2G7ui1PeBxBPKHYARIVTWred8j6AeEKxAyAq2mvdtmO7uS9OeR9APKHYARAVLpe0aJHv+2HZtd3cl/Za0D0e6c47ozsmAIFR7ACIipISacYM38/Zud3cF28Lep8+vp8vKjI6tmhBB+yBYgdAxLWXr7NgQewUOl75+VJ5uVRc7Pv5igoydwC7IGeHnB0gopycS+Pk9wbYHTk7AGzDybk0Tn5vgJNQ7ACIKCfn0jj5vQFOQrEDIKKcnEvj5PcGOAnFDoCIcnIujZPfG+AkFDsAIsop+Tq+mMncWbAgNt8b4CQUOwAiykn5Or60l7lTUED7OWA1ih0AEePEfB1f8vONs1e+kLcDWI+cHXJ2gIiIpwyaeHqvgF2QswPAcvGUQRNP7xWIRRQ7ACIinjJo4um9ArGIYgdARMRTBk08vVcgFlHsAIgIbwaNP07KoCFvB7A3ih0AEdE8g6a1WM/XaS1Q3o7T3isQiyh2AESE2y1lZEiZmW2fc0K+Tmv+8nZSU6Vp04xt4XZbMzYg3lHsAAi7khKjFTs3V6qqMpZlZEjTp0tbthgt2E4qdLzy86XycuM9XnaZsay21jirk5trbBPydoDoo9gBEFb+ggQ//dS41HPsmLMv57hcxnv829/aPkfAIGANQgUJFQTChnA9tgEQLYQKArAE4XpsA8CObFfsLFu2TP3791fnzp2Vk5Ojt99+O+D6ixcv1oUXXqguXbooKytLM2bM0BdffBGl0QJojnA9tgFgR7YqdtatW6eCggIVFRVpx44dGjRokEaOHKnDhw/7XP+5557TzJkzVVRUpN27d+s3v/mN1q1bpwceeCDKIwcgEa4nsQ0AO7LVnJ2cnBxdeeWVWrp0qSSpsbFRWVlZuueeezRz5sw260+dOlW7d+9WaWlp07L//M//1FtvvaU333zT58+or69XfX1909e1tbXKyspizg4QBt75KhUVxuWa1uJhvgrbAIiOmJyz09DQoO3btysvL69pWWJiovLy8lRWVubzNVdddZW2b9/edKnrX//6l1555RXdcMMNfn/O3LlzlZ6e3vTIysoK7xsB4lg8BQn6Q8AgYD+2KXaOHDkit9utzFYJZJmZmaqsrPT5mttuu00PP/ywvvWtb6lTp046//zzNWLEiICXsQoLC1VTU9P02L9/f1jfBxDvRo+Wxo1ru9yJQYL++AsYPOccac4cYxsBiB7bFDuh2Lp1qx5//HH96le/0o4dO1RSUqKXX35ZjzzyiN/XJCcnKy0trcUDQHh4wwSfffb0sowMqbjYuUGC/ngDBptfgT92TCoqIlwQiLYzrB6AV7du3eRyuVTljVv9SlVVlXr27OnzNQ899JB+9KMf6c4775QkXXrppTp+/Lh+/OMfa9asWUpMjOlaDogp3jDB1vNUPv3UOJsxcGB8FTuStHGj9OSTbZd7wwXj5UwXYDXbVANJSUkaMmRIi8nGjY2NKi0t1bBhw3y+5sSJE20KGtdXF8JtNO8acDy327j/k69/dt5l06fH172h2CaAfdim2JGkgoICrVy5UmvWrNHu3bt199136/jx45o0aZIkafz48SosLGxaf9SoUXrqqae0du1a7d27V5s3b9ZDDz2kUaNGNRU9ACKPIL222CaAfdjmMpYkjR07VtXV1Zo9e7YqKyuVnZ2tTZs2NU1a3rdvX4szOQ8++KASEhL04IMPqqKiQt27d9eoUaP02GOPWfUWgLhEkF5bbBPAPmyVs2MF7o0FdNzWrcZdvduzZYs0YkSkR2MPbBMgsmIyZwdA7Bo+3Ggtb50r45WQIGVlGevFC7YJYB8UOwA6zBuk5y8xWIq/ID3CBQH7oNgB0GFut5Gnc+65bZ+LpzDB1vyFC551FuGCQDRR7ADoEG+QYG6u9MknxrJzzjHaqrdsib8wwda84YLFxVJSkrGsro5wQSCaKHYAhMwbJNi6xfqzz4xLOMeOcZlGMsIF58yRGhpaLveGC1LwAJFFNxbdWEBIvHf39pclw929DWwnIDLoxgIQcYTmmcN2AqxHsQMgJITmmcN2AqxHsQMgJL16hXc9p2I7Adaj2AEQEkLzzGE7Adaj2AEQkuahea0RmndaoHBBL7YTEFkUOwBClp8vrVrVdnk8Bwn64i9c8Mwz2U5ANFDsAAiZ2306SDAzU3r2WYIE/fGGC27ZIt1/v7EsJUX64gvjpqFut5WjA5yNYgdASLzJyXPmGF9XVUkzZxIkGIjLZdzh/LLLjK+rq6Vx44z0adKUgcih2AEQNH/JySQCt6+kRPrhD9suZ9sBkUOCMgnKQFBIBA4d2w4IHxKUAUQMicChY9sB1qDYARAUEoFDx7YDrEGxAyAoJAKHjm0HWINiB0BQSAQOHdsOsAbFDoCgeBOBfbU2kJwcWKA0ZbYdEDkUOwCClp8v/fu/t11OcnL7/KUpZ2ay7YBIodgBEBS320j8/dvfjK8ff1x67jmSk4PRPE35oouMZddfL2VkkKQMRALFDgDTvKnJubnSkSPGsqVLpeRkIxmYyy/muVxG2nRFhfH16tUkKQORQrEDwBR/qcmHDpH8Gwrv9qytbbmcJGUg/EhQJkEZaBfJv+HF9gQ6jgRlAGFF8m94sT2B6KLYAdAukn/Di+0JRBfFDoB2kfwbXmxPILoodgC0i+Tf8GJ7AtFFsQOgXc2Tf1sj+Td4gZKUvdieQPhQ7AAwJT9fWr687XJSk0PjL0k5JYXtCYQbxQ4AU9xu6ZNPjP/v21d69llSkzuqeZLyrFnGsi5dpC++MFKqSVMGwoNiB0C7vMnJjz9ufH3ggDRzppEAzKWWjnG5jPTpSy4xvj56VBo3jjRlIJwodgAE5C85maTf8CkpMQqc1tjGQHiQoEyCMuAXSb+RxzYGQkOCMoCwIOk38tjGQORR7ADwi6TfyGMbA5FHsQPAL5J+I49tDEQexQ4Av0j6jTy2MRB5FDsA/PIm/fpqYyA5OTwCpSmzjYHwoNgBEFB+vvSd77RdTnJy+PhLU+7Zk20MhAPFDgC/3G4jyfe994yvZ82SnnuO5ORIaJ6mfN55xrLvflfKyCBJGegoih0APnlTk3NzT98mYtUqKTnZSPzlskr4uVxGKnV1tfH1ihUkKQPhQLEDoA1/qcmVlST6RpJ3u9fVtVxOkjLQMSQok6AMtECirzXY7kBwSFAGEDISfa3Bdgcih2IHQAsk+lqD7Q5EDsUOgBZI9LUG2x2IHIodAC2Q6GsNtjsQORQ7AFponujbGom+kRMoSdmL7Q6EhmIHQBv5+dLvftd2OanJkeUvSfmss9juQEdQ7ABow+2WqqqM/09NlZ55htTkaGmepDxjhrGsa1epvt5IsyZNGQgexQ6AFrzJyd4P2ro6qbDQSPblEkp0uFxGSvVllxlff/KJdNttpCkDoaLYAdDEX3IyCb7RV1Ii3X572+XsCyB4JCiToAxIIsHXTtgXQPtiOkF52bJl6t+/vzp37qycnBy9/fbbAdf/7LPPNGXKFPXq1UvJycn6+te/rldeeSVKowWcgwRf+2BfAOF1htUDaG7dunUqKCjQ8uXLlZOTo8WLF2vkyJHas2ePevTo0Wb9hoYGXXvtterRo4c2bNigPn366JNPPtHZZ58d/cEDMY4EX/tgXwDhZatiZ+HChZo8ebImTZokSVq+fLlefvllrVq1SjNnzmyz/qpVq3Ts2DFt27ZNnTp1kiT1798/4M+or69XfX1909e1tbXhewNADCPB1z7YF0B42eYyVkNDg7Zv3668vLymZYmJicrLy1NZWZnP1/z+97/XsGHDNGXKFGVmZmrgwIF6/PHH5Q7Qmzl37lylp6c3PbKyssL+XoBYRIKvfbAvgPCyTbFz5MgRud1uZWZmtliemZmpyspKn6/517/+pQ0bNsjtduuVV17RQw89pAULFujRRx/1+3MKCwtVU1PT9Ni/f39Y3wcQq7wJvr5aFkhOjq5AacrsCyB4til2QtHY2KgePXro17/+tYYMGaKxY8dq1qxZWr58ud/XJCcnKy0trcUDgCE/Xxo/vu1ykpOjz1+acu/e7AsgWLaZs9OtWze5XC5VeWNbv1JVVaWePXv6fE2vXr3UqVMnuZr9eXPRRRepsrJSDQ0NSkpKiuiYASdxu43unvfeM77+yU+ka64x5oUMH85ZBCvk50ujRxv75aabpKNHjXDBjAxjf7FPAHNsc2YnKSlJQ4YMUWlpadOyxsZGlZaWatiwYT5fc/XVV+vjjz9WY2Nj07IPP/xQvXr1otABguBNTc7Nld5911j24otScrKR5MuHqnVcLiO9+uRJ4+t580hSBoJlm2JHkgoKCrRy5UqtWbNGu3fv1t13363jx483dWeNHz9ehYWFTevffffdOnbsmKZNm6YPP/xQL7/8sh5//HFNmTLFqrcAxBx/qcnV1ST12oF3/5w40XI5ScqAeba5jCVJY8eOVXV1tWbPnq3KykplZ2dr06ZNTZOW9+3bp8TE0/VZVlaWXn31Vc2YMUOXXXaZ+vTpo2nTpun++++36i0AMcXtlqZN8z0p2eMxJsNOn25cSuHsTvSxf4Dw4HYR3C4CcWzrVuOSSHu2bDEuZyG62D+AfzF9uwgA0UNSr72xf4DwoNgB4hhJvfbG/gHCg2IHiGMk9dob+wcID4odII41T+ptjaRe6wVKUvZi/wDto9gB4lx+vvT881Jiq98GpCbbg78k5fR09g9gFsUOEOfcbqmuTmpsNM4QPP200d2zdy8fpHaRny+Vlxv7ZcIEY9nXvibV1xsdWwHufQxAFDtAXPMmJ3+V2ym3W3roISOxl0sj9uJyGe3ll11mfL19u3HrCNKUgfZR7ABxyl9yMsm89lVSIv3sZ22Xs8+AwAgVJFQQccjtNs4GtC50vBISjDk7e/dyhscu2GdAS4QKAgjojTf8f2hKxq0I9u831oM9sM+A0FHsAHGIZN7Ywz4DQkexA8QhknljD/sMCB3FDhCHSOaNPewzIHQUO0AcIjk59gRKU2afAYF1qNg5deqU9u/frz179ujYsWPhGhOAKMjPl+66q+1ykpPty1+aMvsMCCzoYqeurk5PPfWUrrnmGqWlpal///666KKL1L17d5177rmaPHmy3nnnnUiMFUCYuN1G8u7f/mZ8PW6c9NxzJCfHAm+a8ubNUqdOxrKf/lTKyCBJGfAnqGJn4cKF6t+/v55++mnl5eXppZde0s6dO/Xhhx+qrKxMRUVF+vLLL3Xdddfp+uuv10cffRSpcQMIkTc1OTdX+vOfjWWvviolJxsJvVwGsT+XS6qtPX0/s8JCkpSBQIIKFbz11lv14IMP6pJLLgm4Xn19vZ5++mklJSXp9ttv7/AgI4lQQcQTb2py63/13jkfXAqJDexHILjP75ATlOvq6pSamhrSAO2EYgfxggReZ2A/AoaoJCgPHz5clZWVob4cQJSRwOsM7EcgeCEXO5dffrlycnL0wQcftFi+c+dO3XDDDR0eGIDwIoHXGdiPQPBCLnaefvppTZw4Ud/61rf05ptv6sMPP9Qtt9yiIUOGyMW5U8B2SOB1BvYjELwzOvLi4uJiJScn69prr5Xb7dZ//Md/qKysTEOHDg3X+ACEiTeBt6Ki7cRW6fRcDxJ47Y39CAQv5DM7VVVVmjZtmh599FFdfPHF6tSpkyZOnEihA9gUqcnOQJIyELyQi50BAwbo9ddf1/PPP6/t27frhRde0I9//GPNmzcvnOMDEEbeBN7WH4Qk8MYWf0nKZ5/NfgR8CbnYWbVqld59913deOONkqTrr79eW7Zs0aJFizRlypSwDRBA+Ljd0qlTp5N2V64kNTlWeZOUt2wxMnck6dJLpfp6Ix2bNGXgtJCLnR/84Adtlg0ePFjbtm3TH//4xw4NCkD4eZOTm//TLS6Wjh3jkkescrmM1OvsbOPr11+XbruNNGWgtaCKnX379rW7Tv/+/bVt2zZJUkVFRWijAhBW3sTd1vksFRXGcj4UY1dJifTQQ22Xs2+B04Iqdq688kr95Cc/CXijz5qaGm3YsEEDBw7UCy+80OEBAugYt1uaNs1354532fTpXPaIRexbwJygWs/ff/99PfbYY7r22mvVuXNnDRkyRL1791bnzp316aef6v3339c//vEPDR48WD//+c8JFwRsIJjE3REjojYshAH7FjAnqDM7Xbt21cKFC3Xo0CEtW7ZMF1xwgY4cOdJ0d/Nx48Zp+/btKisro9ABbILEXedi3wLmhBQq2KVLF6WmpuqBBx5Qjx49wj0mAGFE4q5zsW8Bc0K+63lKSorq6+uVmZmp7OxsXX755br22ms1IsbOlXLXczid9y7Z7SXucpfs2MO+RTyLyl3P6+rqtGvXLs2bN08DBw7UW2+9peuvv165ubk6fvx4qN8WQJiRnOxcpCkD5oRc7Bw9elQDBw7UuHHj9POf/1yvvfaa9u3bp1OnTumRRx4J5xgBdFB+vnTXXW2Xk5wc+/ylKbNvgdNCvoyVmJionj17atCgQU2P7OxsHT9+XDfccIMOHz4c7rFGBJex4HRut9GNM2uWtG2bNG6cdOONxjyO4cP5q98p3G4jOfnGG40U5Ucfla6+mn0M5wrm8zvku55/9NFH2rVrl/72t79p165dWr9+vcrLy5WUlKRTp07phz/8oXJycpSdna3h3H4XsERJiZHD0rw9+f/9P+Ov/RibXod2uFxSTc3py1cPPmj8t29f41IXZ3gQz0I+s+NLbW2ttmzZou9973u69dZbtWfPHr3//vs6ceJEuH5E2HFmB07lTU1u/S/c+2HIJQ5nYX8j3gTz+R1ysZORkaHs7OymS1iXXnqpzjrrLC1cuFB//OMfm7J33G63XDY+h0qxAyfydun4C5yjS8dZ2N+IR1G5jLVq1Srt2rVLu3bt0saNG1VeXi7JaElfv35903p2LnQApyJZN76wv4HAQi52xowZozFjxjR9XVdXp0OHDqlPnz4688wzwzE2ACEiWTe+sL+BwEIudlpLTU1VampquL4dgA4gWTe+sL+BwELO2QFgX8OHG3M0WgfNeSUkSFlZxnqIfexvIDCKHcCBSE2OL4GSlL3Y34hnFDuAQ+XnS2vXtv3wI1nXmfwlKaelsb8Bih3Aodxu6fBhoxOnSxfpt7+Vtmwx2o/54HOm/HypvNzYz97bg/TqZSQqb91qHBNAPKLYARyopMTIXbnnHuPrkyelBx6Qjh3jUobTuVxGe/ngwcbXe/ZIt90m5eYax0RJiZWjA6xBsQM4jDdJt3XuSkWFsZwPO+crKZF+8pO2yzkGEK/CeruIWESCMpyEJF1wDCBeBPP5zZkdwEGCSdKFM3EMAG1R7AAOQpIuOAaAtih2AAchSRccA0BbFDuAg5CkC44BoC2KHcBBvEm6vtoOSE6OD4HSlDkGEK8odgAHcbuljAzp4ovbPkdycvwIlKY8Z440erQlwwIsQ7EDOIQ3SDA3V3r/fWNZWpo0fTrJyfHIm6ZcXCydcYaxrKZGKioiXBDxx5bFzrJly9S/f3917txZOTk5evvtt029bu3atUpISNCYMWMiO0DAZvwFCdbVGZc0SE6OTxs3Gmdyvvyy5XLCBRFvbFfsrFu3TgUFBSoqKtKOHTs0aNAgjRw5UocPHw74uvLycv3sZz/TcGbdIc643dK0ab7n6XiXTZ/OfZHiDccFcJrtip2FCxdq8uTJmjRpki6++GItX75cKSkpWrVqld/XuN1ujRs3TsXFxTrvvPOiOFrAeoTIwReOC+A0WxU7DQ0N2r59u/Ly8pqWJSYmKi8vT2VlZX5f9/DDD6tHjx6644472v0Z9fX1qq2tbfEAYhkhcvCF4wI4zVbFzpEjR+R2u5WZmdlieWZmpiorK32+5s0339RvfvMbrVy50tTPmDt3rtLT05seWVlZHR43YCVC5OALxwVwmq2KnWDV1dXpRz/6kVauXKlu3bqZek1hYaFqamqaHvv374/wKIHIIkQOvnBcAKedYfUAmuvWrZtcLpeqqqpaLK+qqlLPnj3brP/Pf/5T5eXlGjVqVNOyxsZGSdIZZ5yhPXv26Pzzz2/xmuTkZCUnJ0dg9IA1vCFyN93U9jlC5OJX8+MiIcH3RGWOC8QLW53ZSUpK0pAhQ1RaWtq0rLGxUaWlpRo2bFib9b/xjW/ovffe086dO5se3/3ud5Wbm6udO3dyiQpxY/Ro6b772i4nSDC++QsXTE42OrUyMujGQnywVbEjSQUFBVq5cqXWrFmj3bt36+6779bx48c1adIkSdL48eNVWFgoSercubMGDhzY4nH22WcrNTVVAwcOVFJSkpVvBYgKb5jgk0+eXpaRYYTJESQIb7jgli3S979vLKuvN87q5OYSMIj4YKvLWJI0duxYVVdXa/bs2aqsrFR2drY2bdrUNGl53759Sky0XY0GWMIbJtj6EsWnnxphcgMHUuzAuFR17JjvosYbMMgZQDhZgsfj60pu/KitrVV6erpqamqUlpZm9XAA09xu469yf1kqCQnGZay9e5mXEe84VuBEwXx+c4oEiFGExsEsjhXEO4odIEYRGgezOFYQ7yh2gBhFaBzM4lhBvKPYAWIUoXEwi2MF8Y5iB4hhkyf7DosjTBDNeQMGJd8Fj8cjLVjAsQLnotgBYpA3W6eoyPfzhAmiNX8Bg14FBeTtwLkodoAY483W8dddQ5gg/MnPlxYt8v2cN2+HggdORM4OOTuIIeSloCM4fuAk5OwADkVeCjqC4wfximIHiCHkpaAjOH4Qryh2gBhCXgo6guMH8YpiB4gh5KWgIzh+EK8odoAY0jwvpTWyddCe9vJ2JI4fOBPFDhBjRo+WZs9u+2FFtg7M8Je3k5IiTZsmZWQYXVuAk1DsADHEGyZYXHw6OTkjg2wdBCc/Xyovl7Zska691lh24oRxVic31zjGyNuBk1DsADHCX5jgp59Kc+ZIGzdaMizEKJdLOnZMeu21ts8RMAinIVSQUEHEAMLgEG4cU4h1hAoCDkMYHMKNYwrxhGIHiAGEwSHcOKYQTyh2gBhAGBzCjWMK8YRiB4gBhMEh3DimEE8odoAYMXny6Xbz5ggTRCjaCxj0eKQFCzim4AwUO4DNebN1iop8P0+YIELlL2DQq6CA9nM4A8UOYGP+snW8CBNER+XnS4sW+X6OvB04BTk75OzApshBQTRwnCFWkbMDOAA5KIgGjjPEA4odwKbIQUE0cJwhHlDsADZFDgqigeMM8YBiB7ApclAQDRxniAcUO4BNuVxGlwzZOogkM3k7d94Z3TEB4UaxA9hUSYk0Y4bv58jWQTi1l7dTVGR0bNGCjlhFsQPYUHv5OgsWUOggvPLzpfJyI7vJFzJ3EMvI2SFnBzZD7gmswrGHWELODhDDyD2BVTj24FQUO4DNkHsCq3DswakodgCbIfcEVuHYg1NR7AA2c9VVUvfu/p8n9wSR0l7mjmQ8z7GHWEOxA9hISYl0/vlSdbXv58nXQSS1l7kjSSdPShs3Rm9MQDhQ7AA20V67uUS+DiLPm7mTkeH7+WPHaEFH7KH1nNZz2EB7Lb+ScWnrwAEpKSlqw0KcogUdsYDWcyDGtNfyKxmXtrZti854EN9oQYfTUOwANkDLL+yE4xFOQ7ED2AAtv7ATjkc4DcUOYAPell9/aDdHNJlpQe/e3YhJAGIBxQ5gAxs3Gi29vtBujmgz04JeXW3EJNCVhVhAsQNYzNtyfvSo7+czMmg3R/R5W9D79PG/DndCR6yg9ZzWc1jITMt5375SeTlndWCNhgbjGAwUdEkbOqxA6zkQI8y0nB84QIsvrLNtm/9CR6INHbGBYgewEC2+sDuOUTgBxQ5goR49zK1Hiy+sQhs6nIBiB7BISYk0YULgdWg5h9XMtKG7XNKRI9EbExAsih3AAt4OrIoK/+vQcg47aN6G7o/bLd1yC11ZsC+KHSDK3G5p2jRjYmcgffrQcg57yM+X1q1rv+iePt04vgG7odgBosxMB5YkrV5NoQP76N49cCFDVxbsjGIHiDKzXSuHD0d2HEAw6MpCLKPYAaKM7hbEIrPHo9kOQyCabFnsLFu2TP3791fnzp2Vk5Ojt99+2++6K1eu1PDhw3XOOefonHPOUV5eXsD1AatVVwee+0AHFuzITFeWJE2cyERl2I/tip1169apoKBARUVF2rFjhwYNGqSRI0fqsJ9z+lu3btWtt96qLVu2qKysTFlZWbruuutUEajNBbBISYk0dmz7kzjpwILdmLk5qMT9smBPtrs3Vk5Ojq688kotXbpUktTY2KisrCzdc889mjlzZruvd7vdOuecc7R06VKNHz++3fW5Nxaixcx9sFwuae1a48MCsKOSEunee9uPTeB+WYi0mL03VkNDg7Zv3668vLymZYmJicrLy1NZWZmp73HixAmdOnVKGRkZPp+vr69XbW1tiwcQDWa6sNxuqVu36IwHCEV+vrRmTeB16MyC3diq2Dly5IjcbrcyMzNbLM/MzFRlZaWp73H//ferd+/eLQqm5ubOnav09PSmR1ZWVofHDZhBNwucwmynIMcy7MJWxU5HPfHEE1q7dq1efPFFde7c2ec6hYWFqqmpaXrs378/yqNEvKILC07BsYxYc4bVA2iuW7ducrlcqqqqarG8qqpKPXv2DPja+fPn64knntBrr72myy67zO96ycnJSk5ODst4gWB4u7D8TU72znOgCwt25+3MqqjwnwTO/bJgJ7Y6s5OUlKQhQ4aotLS0aVljY6NKS0s1bNgwv6/7+c9/rkceeUSbNm3SFVdcEY2hAkGhCwtOwv2yEGtsVexIUkFBgVauXKk1a9Zo9+7duvvuu3X8+HFNmjRJkjR+/HgVFhY2rf/kk0/qoYce0qpVq9S/f39VVlaqsrJSn3/+uVVvAWjBzL2wXC5p/XpuD4HYwf2yEEtsdRlLksaOHavq6mrNnj1blZWVys7O1qZNm5omLe/bt0+JiadrtKeeekoNDQ26qVWvblFRkebMmRPNoQM+0YUFpwrmflkjRkRtWEAbtit2JGnq1KmaOnWqz+e2bt3a4uvy8vLIDwjoALqw4FQc24gVtruMBTiN2XsF0bmCWMP9shArKHaACCopkSZMCLwO98JCrOJ+WYgVFDtAhJSUGLd9aC9WX6ILC7GJ+2UhVlDsABFgpgNLkvr0kTZsoAsLsSs/3ziGe/f2v4733wGdWbAKxQ4QAWY6sCRp9WoKHcQ+7pcFu6PYASLAbPeJ2XsMAXbH/bJgZxQ7QAR89JG59ejAglOYPZbN/tsAwoliBwizkhKpqCjwOnRgwWnMdmbNmcNEZUQfxQ4QRt6JyWbQgQUn8XZmtTcpX2KiMqKPYgcIo61bzU1MnjOHiclwnvx8qbg48DpMVIYVKHaAMCkpMe7ybMYFF0R2LIBVzB7bGzdGdhxAcxQ7QBh4AwSPHTO3PhOT4VRmj+3Fi5m7g+ih2AE6yGyAoMTEZDifd6JyexISmLuD6KHYATrIbICgFxOT4WTNbyERCHN3EE0UO0AHmQ1J69qVW0MgPuTnG2dtzAh07zggXCh2gA4yG5K2bh2FDuLH6NHm1psxg7k7iDyKHaADggkQHDEiKkMCbMFsyOCRI9wRHZFHsQOEiABBwL9g5u5ITFZGZFHsACEiQBAILD/fmKfWrVvg9ZisjEij2AFCQIAgYE5+vnFm0wyCBhEpFDtAkAgQBILTp4+59QgaRKRQ7ABBIEAQCB5Bg7AaxQ4QBAIEgeAFGzS4dWvEh4Q4Q7EDBMHsnAICBIGWggkavOUWLmchvCh2AJNKSsxPtCRAEGjLbNDgsWNk7yC8KHYAExoapLvuan89AgQB/8wGDUrGJa1p05i/g/Cg2AHaUVJidJNUV7e/rsfDPB3AH7Nzd7wOHJAeeyxy40H8oNgBAvC2mR85Ym796dO5fAUE4g0azMgwt35REZez0HEUO4AfwbSZe5mdkwDEs/x8af168+vfdZdxKRkIFcUO4Mdjj5lvMydTBwjOiBHmsnck4xJy376c4UHoKHYAH8zczbw15uoA5gU7f6e6mg4thI5iB2jFbOeVV/fuZOoAocjPl4qLza9PhxZCRbEDNBNM55VkFDoHDlDoAKGaNcv85SyJDi2EhmIH+EqwnVeStHy5lJQUuTEBTue9nGUme8eLDi0Ei2IHUGidV8XFnNEBwsHbjt6tm/nX0KGFYFDsAAqu80oyTrvPmhW58QDxJj9fqqgwLg2bQYcWgkGxg7jmdksPPxxc51VCgnHanc4rILySkoxLw2ZVV0vf/770/PORGxOcgWIHcaukRDr33OAKHTqvgMgKtkNLkm691fh3CfhDsYO4tGGD8RdhRYX519B5BURHsB1abrd0883GWVra0uELxQ7izvPPSz/4QfCvo/MKiI5QOrQk4yxt//7M40FbFDuIG975ObfcEvxff3ReAdEVSoeWZJx9ZR4PWkvweIJptnWe2tpapaenq6amRmlpaVYPBxFSUiLde29wl628+vaVysuZkAxYoaHB+DdoNujTy+WS1q41srPgTMF8fnNmB44XyvwcLzqvAGsF26HlxTweNEexA0dyu6WtW42gwLFjQ/seffvSeQXYQX6+tH59aH90FBVJPXpQ9MQ7ih04TkmJMUkxN1f65S+lxsbgv0dxsXHpikIHsIebbzYuS4Xi2DGj6MnMZPJyvKLYgaN4L1kFk4bcnMtlTGycPZtLV4Dd3HST9MILxs16Q3H0qPH7gbM88YdiBzEvHJesvP7nf5jQCNhZfr70ySfBBw82x6Wt+EM3Ft1YMcvtNu5p9YtfGKepO6JvX+P7cNkKiB3PP2+kJ3ekYElLk26/XRo9Who+nDO6sYRuLDiW9yzOjBlSRobxF1pHCx3m5wCxqSPzeLxqa6XFi405fpztcS7O7HBmJyaE8yyOFzkcgDN0JEfLF872xAbO7MARInEWpznm5wDOEI55PM1xtsd5OLPDmR1bcLulN96QDh0yfrm88Ya0ZEl4ixuvrCzjFxmXrQDnKSmRfvxjo/MqnNLSpIkTpQEDjJsC9+nDWR+rBfP5TbFDsWMJb3FTUSGVlkobN0amsPFKTJTuuUcaM4ZfUIDTeS97L14sffpp5H5Ot27SbbdRAFmFYicIFDvh1byIqa42fgH07Gk8V1lpLCsvl557Lvh73XTE+vXGZEYA8cNb9BQVRe9nNi+AunY1zjA1/z14+LDUqxdFUThQ7ASBYsfQ+jKSdLo48VWw2KWIaQ+XrABE6tJWR2RkGGebhw8P/nctZ5EMFDtB8G6sjRtrdOaZaSEddOFc5usvgUj//EjOj7ECnRQAWotER6fVWl9Gs+Izy8rPsf37a1VYGMPFzrJlyzRv3jxVVlZq0KBBWrJkiYYOHep3/eeff14PPfSQysvLdcEFF+jJJ5/UDTfcYOpneYsdqUZS/J7ZcYKMDCNFedYsChwAvnnPYm/cKK1aZXReIVbVSorR1vN169apoKBARUVF2rFjhwYNGqSRI0fq8OHDPtfftm2bbr31Vt1xxx169913NWbMGI0ZM0Z///vfozxyWCEtTZo+XdqyxbgWzj2tAATickkjRkiLFhlneIqLjT+U4Gy2O7OTk5OjK6+8UkuXLpUkNTY2KisrS/fcc49mzpzZZv2xY8fq+PHj+sMf/tC07Jvf/Kays7O1fPnydn8eZ3ZiE2dxAIQLZ3tiVYye2WloaND27duVl5fXtCwxMVF5eXkqKyvz+ZqysrIW60vSyJEj/a5fX1+v2traFg/EBs7iAIgEzvY4n62KnSNHjsjtdiszM7PF8szMTFVWVvp8TWVlZVDrz507V+np6U2PrKys8AweEZORYfzyOXbM+GU0YgRFDoDIcLmMP6QOHzb+sJo+3ZgYi9h2htUDiLbCwkIVFBQ0fV1bW0vBYyPN2zHJowBgFe/ZnhEjpPnzW+aH2TFmA4HZqtjp1q2bXC6XqqqqWiyvqqpST2+/WSs9e/YMav3k5GQlJyeHZ8DokO7dpVtvJX0UgL15C5/mFiygAIoltip2kpKSNGTIEJWWlmrMmDGSjAnKpaWlmjp1qs/XDBs2TKWlpZo+fXrTss2bN2vYsGFRGDF8aV3EEIgFwGnMFECt82aclmkWS2zXjbVu3TpNmDBBK1as0NChQ7V48WKtX79eH3zwgTIzMzV+/Hj16dNHc+fOlWS0nl9zzTV64okndOONN2rt2rV6/PHHtWPHDg0cOLDdn0c3VkukegJA5Dg1rd4a5ruxbHVmRzJayaurqzV79mxVVlYqOztbmzZtapqEvG/fPiUmnp5XfdVVV+m5557Tgw8+qAceeEAXXHCBXnrpJVOFTnMbN0pnnhk/yZOtlzE/BgAiz9cZoVC0PosUnwnKUmGhue1luzM70ca9sQAAiD3BfH7bqvUcAAAg3Ch2AACAo1HsAAAAR6PYAQAAjkaxAwAAHI1iBwAAOBrFDgAAcDSKHQAA4GgUOwAAwNFsd7uIaPMGSNfW1lo8EgAAYJb3c9vMjSDivtipq6uTJGVlZVk8EgAAEKy6urqvbujtX9zfG6uxsVEHDx5UamqqEhISrB5OyGpra5WVlaX9+/dzjy+LsS/sg31hH+wLe3HC/vB4PKqrq1Pv3r1b3CDcl7g/s5OYmKi+fftaPYywSUtLi9kD12nYF/bBvrAP9oW9xPr+aO+MjhcTlAEAgKNR7AAAAEej2HGI5ORkFRUVKTk52eqhxD32hX2wL+yDfWEv8bY/4n6CMgAAcDbO7AAAAEej2AEAAI5GsQMAAByNYgcAADgaxY6D1dfXKzs7WwkJCdq5c6fVw4k75eXluuOOOzRgwAB16dJF559/voqKitTQ0GD10OLGsmXL1L9/f3Xu3Fk5OTl6++23rR5S3Jk7d66uvPJKpaamqkePHhozZoz27Nlj9bAg6YknnlBCQoKmT59u9VAijmLHwe677z717t3b6mHErQ8++ECNjY1asWKF/vGPf2jRokVavny5HnjgAauHFhfWrVungoICFRUVaceOHRo0aJBGjhypw4cPWz20uPKnP/1JU6ZM0V/+8hdt3rxZp06d0nXXXafjx49bPbS49s4772jFihW67LLLrB5KVNB67lD/93//p4KCAr3wwgu65JJL9O677yo7O9vqYcW9efPm6amnntK//vUvq4fieDk5Obryyiu1dOlSScZ98LKysnTPPfdo5syZFo8uflVXV6tHjx7605/+pH/7t3+zejhx6fPPP9fgwYP1q1/9So8++qiys7O1ePFiq4cVUZzZcaCqqipNnjxZzzzzjFJSUqweDpqpqalRRkaG1cNwvIaGBm3fvl15eXlNyxITE5WXl6eysjILR4aamhpJ4t+BhaZMmaIbb7yxxb8Pp4v7G4E6jcfj0cSJE3XXXXfpiiuuUHl5udVDwlc+/vhjLVmyRPPnz7d6KI535MgRud1uZWZmtliemZmpDz74wKJRobGxUdOnT9fVV1+tgQMHWj2cuLR27Vrt2LFD77zzjtVDiSrO7MSImTNnKiEhIeDjgw8+0JIlS1RXV6fCwkKrh+xYZvdFcxUVFbr++ut18803a/LkyRaNHLDWlClT9Pe//11r1661eihxaf/+/Zo2bZp+97vfqXPnzlYPJ6qYsxMjqqurdfTo0YDrnHfeebrlllv0v//7v0pISGha7na75XK5NG7cOK1ZsybSQ3U8s/siKSlJknTw4EGNGDFC3/zmN7V69WolJvI3RqQ1NDQoJSVFGzZs0JgxY5qWT5gwQZ999pk2btxo3eDi1NSpU7Vx40a9/vrrGjBggNXDiUsvvfSSvve978nlcjUtc7vdSkhIUGJiourr61s85yQUOw6zb98+1dbWNn198OBBjRw5Uhs2bFBOTo769u1r4ejiT0VFhXJzczVkyBA9++yzjv1FYkc5OTkaOnSolixZIsm4hNKvXz9NnTqVCcpR5PF4dM899+jFF1/U1q1bdcEFF1g9pLhVV1enTz75pMWySZMm6Rvf+Ibuv/9+R19aZM6Ow/Tr16/F12eddZYk6fzzz6fQibKKigqNGDFC5557rubPn6/q6uqm53r27GnhyOJDQUGBJkyYoCuuuEJDhw7V4sWLdfz4cU2aNMnqocWVKVOm6LnnntPGjRuVmpqqyspKSVJ6erq6dOli8ejiS2pqapuC5swzz1TXrl0dXehIFDtAxGzevFkff/yxPv744zaFJidUI2/s2LGqrq7W7NmzVVlZqezsbG3atKnNpGVE1lNPPSVJGjFiRIvlTz/9tCZOnBj9ASEucRkLAAA4GjMlAQCAo1HsAAAAR6PYAQAAjkaxAwAAHI1iBwAAOBrFDgAAcDSKHQAA4GgUOwAAwNEodgAAgKNR7AAAAEej2AEAAI5GsQPAcaqrq9WzZ089/vjjTcu2bdumpKQklZaWWjgyAFbgRqAAHOmVV17RmDFjtG3bNl144YXKzs7W6NGjtXDhQquHBiDKKHYAONaUKVP02muv6YorrtB7772nd955R8nJyVYPC0CUUewAcKyTJ09q4MCB2r9/v7Zv365LL73U6iEBsABzdgA41j//+U8dPHhQjY2NKi8vt3o4ACzCmR0AjtTQ0KChQ4cqOztbF154oRYvXqz33ntPPXr0sHpoAKKMYgeAI/3Xf/2XNmzYoF27dumss87SNddco/T0dP3hD3+wemgAoozLWAAcZ+vWrVq8eLGeeeYZpaWlKTExUc8884zeeOMNPfXUU1YPD0CUcWYHAAA4Gmd2AACAo1HsAAAAR6PYAQAAjkaxAwAAHI1iBwAAOBrFDgAAcDSKHQAA4GgUOwAAwNEodgAAgKNR7AAAAEej2AEAAI72/wEndUbr0UhvxgAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "\n",
    "data = np.loadtxt('zero_nodes.dat')\n",
    "x = data[:,0]\n",
    "y = data[:,1]\n",
    "\n",
    "plt.xlabel('x')\n",
    "plt.xlim([np.min(x),np.max(x)])\n",
    "\n",
    "plt.ylabel('$\\psi(x)$')\n",
    "plt.plot(x,y,'-o', c='blue', label='0 nodes')\n",
    "plt.legend()\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2243438c",
   "metadata": {},
   "source": [
    "Now we calculate the solution for 1 node, what do you expect to see?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "a81e7f81",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Iteration = 0, number of crossing = 3 and nodes = 0 for pos axis, energy = 6.25\n",
      "Iteration = 1, number of crossing = 1 and nodes = 0 for pos axis, energy = 3.125\n",
      "Iteration = 2, number of crossing = 1 and nodes = 0 for pos axis, energy = 1.5625\n",
      "Iteration = 3, number of crossing = 0 and nodes = 0 for pos axis, energy = 0.78125\n",
      "Iteration = 4, number of crossing = 0 and nodes = 0 for pos axis, energy = 1.171875\n",
      "Iteration = 5, number of crossing = 0 and nodes = 0 for pos axis, energy = 1.3671875\n",
      "Iteration = 6, number of crossing = 0 and nodes = 0 for pos axis, energy = 1.46484375\n",
      "Iteration = 7, number of crossing = 1 and nodes = 0 for pos axis, energy = 1.513671875\n",
      "Iteration = 8, number of crossing = 0 and nodes = 0 for pos axis, energy = 1.4892578125\n",
      "Iteration = 9, number of crossing = 1 and nodes = 0 for pos axis, energy = 1.50146484375\n",
      "Iteration = 10, number of crossing = 0 and nodes = 0 for pos axis, energy = 1.495361328125\n",
      "Iteration = 11, number of crossing = 0 and nodes = 0 for pos axis, energy = 1.4984130859375\n",
      "Iteration = 12, number of crossing = 0 and nodes = 0 for pos axis, energy = 1.49993896484375\n",
      "Iteration = 13, number of crossing = 1 and nodes = 0 for pos axis, energy = 1.500701904296875\n",
      "Iteration = 14, number of crossing = 1 and nodes = 0 for pos axis, energy = 1.5003204345703125\n",
      "Iteration = 15, number of crossing = 1 and nodes = 0 for pos axis, energy = 1.5001296997070312\n",
      "Iteration = 16, number of crossing = 1 and nodes = 0 for pos axis, energy = 1.5000343322753906\n",
      "Iteration = 17, number of crossing = 0 and nodes = 0 for pos axis, energy = 1.4999866485595703\n",
      "Iteration = 18, number of crossing = 1 and nodes = 0 for pos axis, energy = 1.5000104904174805\n",
      "Iteration = 19, number of crossing = 0 and nodes = 0 for pos axis, energy = 1.4999985694885254\n",
      "Iteration = 20, number of crossing = 1 and nodes = 0 for pos axis, energy = 1.500004529953003\n",
      "Iteration = 21, number of crossing = 1 and nodes = 0 for pos axis, energy = 1.5000015497207642\n",
      "Iteration = 22, number of crossing = 1 and nodes = 0 for pos axis, energy = 1.5000000596046448\n",
      "Iteration = 23, number of crossing = 0 and nodes = 0 for pos axis, energy = 1.499999314546585\n",
      "Iteration = 24, number of crossing = 0 and nodes = 0 for pos axis, energy = 1.499999687075615\n",
      "Iteration = 25, number of crossing = 1 and nodes = 0 for pos axis, energy = 1.4999998733401299\n",
      "Iteration = 26, number of crossing = 0 and nodes = 0 for pos axis, energy = 1.4999997802078724\n",
      "Iteration = 27, number of crossing = 0 and nodes = 0 for pos axis, energy = 1.4999998267740011\n",
      "Iteration = 28, number of crossing = 1 and nodes = 0 for pos axis, energy = 1.4999998500570655\n",
      "Iteration = 29, number of crossing = 1 and nodes = 0 for pos axis, energy = 1.4999998384155333\n",
      "Iteration = 30, number of crossing = 0 and nodes = 0 for pos axis, energy = 1.4999998325947672\n",
      "Iteration = 31, number of crossing = 1 and nodes = 0 for pos axis, energy = 1.4999998355051503\n",
      "Iteration = 32, number of crossing = 1 and nodes = 0 for pos axis, energy = 1.4999998340499587\n",
      "Iteration = 33, number of crossing = 1 and nodes = 0 for pos axis, energy = 1.499999833322363\n",
      "Iteration = 34, number of crossing = 1 and nodes = 0 for pos axis, energy = 1.499999832958565\n",
      "Iteration = 35, number of crossing = 1 and nodes = 0 for pos axis, energy = 1.4999998327766662\n",
      "Iteration = 36, number of crossing = 0 and nodes = 0 for pos axis, energy = 1.4999998326857167\n"
     ]
    }
   ],
   "source": [
    "_ = integrate_1D_harm_numerov(5,100,1,'one_node.dat')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "66febfb1",
   "metadata": {},
   "source": [
    "The energy is correct ($1.5$)! Let's compare the nodeless and the one-node solutions: "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "dffb6b78",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x10e553f10>"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "data_one_node = np.loadtxt('one_node.dat')\n",
    "x_one_node = data_one_node[:,0]\n",
    "y_one_node = data_one_node[:,1]\n",
    "\n",
    "plt.xlabel('x')\n",
    "plt.xlim([np.min(x),np.max(x)])\n",
    "\n",
    "plt.ylabel('$\\psi(x)$')\n",
    "plt.plot(x,y,'-o', c='blue', label='0 nodes')\n",
    "plt.plot(x_one_node,y_one_node,'-o', c='red', label='1 node')\n",
    "\n",
    "plt.legend()\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "3b3ded26",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Iteration = 0, number of crossing = 3 and nodes = 2 for pos axis, energy = 6.25\n",
      "Iteration = 1, number of crossing = 1 and nodes = 2 for pos axis, energy = 3.125\n",
      "Iteration = 2, number of crossing = 2 and nodes = 2 for pos axis, energy = 4.6875\n",
      "Iteration = 3, number of crossing = 2 and nodes = 2 for pos axis, energy = 5.46875\n",
      "Iteration = 4, number of crossing = 3 and nodes = 2 for pos axis, energy = 5.859375\n",
      "Iteration = 5, number of crossing = 3 and nodes = 2 for pos axis, energy = 5.6640625\n",
      "Iteration = 6, number of crossing = 3 and nodes = 2 for pos axis, energy = 5.56640625\n",
      "Iteration = 7, number of crossing = 3 and nodes = 2 for pos axis, energy = 5.517578125\n",
      "Iteration = 8, number of crossing = 2 and nodes = 2 for pos axis, energy = 5.4931640625\n",
      "Iteration = 9, number of crossing = 3 and nodes = 2 for pos axis, energy = 5.50537109375\n",
      "Iteration = 10, number of crossing = 2 and nodes = 2 for pos axis, energy = 5.499267578125\n",
      "Iteration = 11, number of crossing = 3 and nodes = 2 for pos axis, energy = 5.5023193359375\n",
      "Iteration = 12, number of crossing = 3 and nodes = 2 for pos axis, energy = 5.50079345703125\n",
      "Iteration = 13, number of crossing = 2 and nodes = 2 for pos axis, energy = 5.500030517578125\n",
      "Iteration = 14, number of crossing = 3 and nodes = 2 for pos axis, energy = 5.5004119873046875\n",
      "Iteration = 15, number of crossing = 3 and nodes = 2 for pos axis, energy = 5.500221252441406\n",
      "Iteration = 16, number of crossing = 3 and nodes = 2 for pos axis, energy = 5.500125885009766\n",
      "Iteration = 17, number of crossing = 2 and nodes = 2 for pos axis, energy = 5.500078201293945\n",
      "Iteration = 18, number of crossing = 3 and nodes = 2 for pos axis, energy = 5.5001020431518555\n",
      "Iteration = 19, number of crossing = 2 and nodes = 2 for pos axis, energy = 5.5000901222229\n",
      "Iteration = 20, number of crossing = 3 and nodes = 2 for pos axis, energy = 5.500096082687378\n",
      "Iteration = 21, number of crossing = 3 and nodes = 2 for pos axis, energy = 5.500093102455139\n",
      "Iteration = 22, number of crossing = 2 and nodes = 2 for pos axis, energy = 5.50009161233902\n",
      "Iteration = 23, number of crossing = 2 and nodes = 2 for pos axis, energy = 5.5000923573970795\n",
      "Iteration = 24, number of crossing = 2 and nodes = 2 for pos axis, energy = 5.500092729926109\n",
      "Iteration = 25, number of crossing = 2 and nodes = 2 for pos axis, energy = 5.500092916190624\n",
      "Iteration = 26, number of crossing = 2 and nodes = 2 for pos axis, energy = 5.500093009322882\n",
      "Iteration = 27, number of crossing = 2 and nodes = 2 for pos axis, energy = 5.50009305588901\n",
      "Iteration = 28, number of crossing = 3 and nodes = 2 for pos axis, energy = 5.500093079172075\n",
      "Iteration = 29, number of crossing = 2 and nodes = 2 for pos axis, energy = 5.500093067530543\n",
      "Iteration = 30, number of crossing = 3 and nodes = 2 for pos axis, energy = 5.500093073351309\n",
      "Iteration = 31, number of crossing = 3 and nodes = 2 for pos axis, energy = 5.500093070440926\n",
      "Iteration = 32, number of crossing = 2 and nodes = 2 for pos axis, energy = 5.500093068985734\n",
      "Iteration = 33, number of crossing = 2 and nodes = 2 for pos axis, energy = 5.50009306971333\n",
      "Iteration = 34, number of crossing = 3 and nodes = 2 for pos axis, energy = 5.500093070077128\n",
      "Iteration = 35, number of crossing = 2 and nodes = 2 for pos axis, energy = 5.500093069895229\n",
      "Iteration = 36, number of crossing = 2 and nodes = 2 for pos axis, energy = 5.500093069986178\n"
     ]
    }
   ],
   "source": [
    "_ = integrate_1D_harm_numerov(5,100,5,'five_nodes.dat')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "78bc6aa2",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x10e775d90>"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.xlabel('x')\n",
    "plt.xlim([np.min(x),np.max(x)])\n",
    "data_five_node = np.loadtxt('five_nodes.dat')\n",
    "x_five_node = data_five_node[:,0]\n",
    "y_five_node = data_five_node[:,1]\n",
    "plt.ylabel('$\\psi(x)$')\n",
    "plt.plot(x,y,'-o', c='blue', label='0 nodes')\n",
    "plt.plot(x_one_node,y_one_node,'-o', c='red', label='1 node')\n",
    "plt.plot(x_five_node,y_five_node,'-o', c='green', label='5 nodes')\n",
    "plt.legend()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "da6f6fb1",
   "metadata": {},
   "source": [
    "Now let's try to increase the $x$ range, does the code still work?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "1d923385",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Iteration = 0, number of crossing = 13 and nodes = 0 for pos axis, energy = 25.0\n",
      "Iteration = 1, number of crossing = 7 and nodes = 0 for pos axis, energy = 12.5\n",
      "Iteration = 2, number of crossing = 3 and nodes = 0 for pos axis, energy = 6.25\n",
      "Iteration = 3, number of crossing = 2 and nodes = 0 for pos axis, energy = 3.125\n",
      "Iteration = 4, number of crossing = 1 and nodes = 0 for pos axis, energy = 1.5625\n",
      "Iteration = 5, number of crossing = 1 and nodes = 0 for pos axis, energy = 0.78125\n",
      "Iteration = 6, number of crossing = 0 and nodes = 0 for pos axis, energy = 0.390625\n",
      "Iteration = 7, number of crossing = 1 and nodes = 0 for pos axis, energy = 0.5859375\n",
      "Iteration = 8, number of crossing = 0 and nodes = 0 for pos axis, energy = 0.48828125\n",
      "Iteration = 9, number of crossing = 1 and nodes = 0 for pos axis, energy = 0.537109375\n",
      "Iteration = 10, number of crossing = 1 and nodes = 0 for pos axis, energy = 0.5126953125\n",
      "Iteration = 11, number of crossing = 1 and nodes = 0 for pos axis, energy = 0.50048828125\n",
      "Iteration = 12, number of crossing = 0 and nodes = 0 for pos axis, energy = 0.494384765625\n",
      "Iteration = 13, number of crossing = 0 and nodes = 0 for pos axis, energy = 0.4974365234375\n",
      "Iteration = 14, number of crossing = 0 and nodes = 0 for pos axis, energy = 0.49896240234375\n",
      "Iteration = 15, number of crossing = 0 and nodes = 0 for pos axis, energy = 0.499725341796875\n",
      "Iteration = 16, number of crossing = 1 and nodes = 0 for pos axis, energy = 0.5001068115234375\n",
      "Iteration = 17, number of crossing = 0 and nodes = 0 for pos axis, energy = 0.49991607666015625\n",
      "Iteration = 18, number of crossing = 1 and nodes = 0 for pos axis, energy = 0.5000114440917969\n",
      "Iteration = 19, number of crossing = 0 and nodes = 0 for pos axis, energy = 0.49996376037597656\n",
      "Iteration = 20, number of crossing = 0 and nodes = 0 for pos axis, energy = 0.4999876022338867\n",
      "Iteration = 21, number of crossing = 0 and nodes = 0 for pos axis, energy = 0.4999995231628418\n",
      "Iteration = 22, number of crossing = 1 and nodes = 0 for pos axis, energy = 0.5000054836273193\n",
      "Iteration = 23, number of crossing = 1 and nodes = 0 for pos axis, energy = 0.5000025033950806\n",
      "Iteration = 24, number of crossing = 1 and nodes = 0 for pos axis, energy = 0.5000010132789612\n",
      "Iteration = 25, number of crossing = 1 and nodes = 0 for pos axis, energy = 0.5000002682209015\n",
      "Iteration = 26, number of crossing = 1 and nodes = 0 for pos axis, energy = 0.49999989569187164\n",
      "Iteration = 27, number of crossing = 1 and nodes = 0 for pos axis, energy = 0.4999997094273567\n",
      "Iteration = 28, number of crossing = 1 and nodes = 0 for pos axis, energy = 0.49999961629509926\n",
      "Iteration = 29, number of crossing = 0 and nodes = 0 for pos axis, energy = 0.4999995697289705\n",
      "Iteration = 30, number of crossing = 0 and nodes = 0 for pos axis, energy = 0.4999995930120349\n",
      "Iteration = 31, number of crossing = 0 and nodes = 0 for pos axis, energy = 0.4999996046535671\n",
      "Iteration = 32, number of crossing = 1 and nodes = 0 for pos axis, energy = 0.49999961047433317\n",
      "Iteration = 33, number of crossing = 0 and nodes = 0 for pos axis, energy = 0.4999996075639501\n",
      "Iteration = 34, number of crossing = 1 and nodes = 0 for pos axis, energy = 0.49999960901914164\n",
      "Iteration = 35, number of crossing = 0 and nodes = 0 for pos axis, energy = 0.4999996082915459\n",
      "Iteration = 36, number of crossing = 0 and nodes = 0 for pos axis, energy = 0.49999960865534376\n",
      "Iteration = 37, number of crossing = 1 and nodes = 0 for pos axis, energy = 0.4999996088372427\n",
      "Iteration = 38, number of crossing = 0 and nodes = 0 for pos axis, energy = 0.49999960874629323\n"
     ]
    }
   ],
   "source": [
    "_ = integrate_1D_harm_numerov(10,100,0,'large_x.dat')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "8e88825f",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x10e79edd0>"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "data_large_x = np.loadtxt('large_x.dat')\n",
    "x_large_x = data_large_x[:,0]\n",
    "y_large_x = data_large_x[:,1]\n",
    "\n",
    "plt.xlabel('x')\n",
    "plt.xlim([np.min(x_large_x),np.max(x_large_x)])\n",
    "\n",
    "plt.ylabel('$\\psi(x)$')\n",
    "plt.plot(x_large_x,y_large_x,'-o', c='purple', label='0 nodes ($x_{max}=10$)')\n",
    "plt.legend()\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "5b7f896f",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x11c83edd0>"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.xlabel('x')\n",
    "plt.xlim([-5,5])\n",
    "plt.ylim([0,1.2])\n",
    "plt.ylabel('$\\psi(x)$')\n",
    "plt.plot(x,y,'-o', c='blue', label='0 nodes ($x_{max}=5$)')\n",
    "\n",
    "plt.plot(x_large_x,y_large_x,'-o', c='purple', label='0 nodes ($x_{max}=10$)')\n",
    "plt.legend()\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "57cf1c6a",
   "metadata": {},
   "source": [
    ">The two solutions are identical around the origin, but the code gives a spurious divergence for large values of $x$!\n",
    "\n",
    "### Lab exercises (tomorrow)\n",
    "\n",
    "* Study how results depend on the input parameters.\n",
    "* Does the maximum number of nodes depend on the grid density?\n",
    "* Implement a comparison between the quantum and classical probability densities.\n",
    "* Try to implement an improved (but more complex) version of the algorithm that does not suffer from this drawback: Fortran codes for the basic (the one above) and improved Numerov's methods are already available on Moodle, start from there!\n",
    "* Try to implement more complex potentials, such as the double-well \n",
    "$$V(x) = a ((x/b)^4 -2(x/b)^2 +1)$$\n",
    "\n",
    "> Remember: except for simple potentials as those used in this tutorial (e.g. harmonic oscillator), in general analytical solutions are not available and one needs to resort to numerical integration methods."
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.11.1"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}