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 },
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 "nbformat_minor": 0,
 "worksheets": [
  {
   "cells": [
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import numpy as np\n",
      "import scipy.sparse as sp\n",
      "import scipy.sparse.linalg as alg\n",
      "import math\n",
      "from time import time\n",
      "\n",
      "import pylab as pl\n",
      "\n",
      "%pylab inline --no-import-all"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Populating the interactive namespace from numpy and matplotlib\n"
       ]
      }
     ],
     "prompt_number": 1
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# x - bezwymiarowa siatka polozen\n",
      "\n",
      "# Stale 'rho' zadeklerowane dla ponizszych typow potencjalow to bezwymiarowe zmienne\n",
      "# z bezwymiarowego rownania Schrodingera.\n",
      "\n",
      "def rho_Konwent():\n",
      "    k = 1.0\n",
      "    return 0.25 * (2 * k + 1)**2\n",
      "def Konwent(x):\n",
      "    # potencjal Konwenta: v(x) = V_c * (alpha * cosh(C*x) - 1)**2\n",
      "    # bezwymiarowy potencjal Konwenta: V(x) = ( (b / (2*k+1)) * cosh(x) - 1 ) ** 2\n",
      "    k = 1.0\n",
      "    b = 0.03   \n",
      "    return  ( (b / (2.0 * k + 1.0)) * np.cosh(x) - 1) ** 2 \n",
      "\n",
      "\n",
      "def rho_Konwent2(m, V_c, C, h):\n",
      "    # 1/C - stala o wymiarze dlugosci\n",
      "    # m - masa czastki\n",
      "    # V_c - charakterystyczna energia\n",
      "    # h - stala Diraca\n",
      "    return 2.0 * m * V_c / (C * C * h * h)\n",
      "def Konwent2(x):\n",
      "    # potencjal Konwenta: v(x) = V_c * (alpha * cosh(C*x) - 1)**2\n",
      "    # bezwymiarowy potencjal Konwenta: V(x) = (apha*cosh(x) - 1)**2\n",
      "    return  (c * np.cosh(x) - 1) ** 2   "
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 2
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# rozmiar macierzy pieciodiagonalnej:\n",
      "N = 1500\n",
      "    \n",
      "# konce bezwymiarowego przedzialu obustronnie domknietego [x_min,x_max]:\n",
      "x_min = -8.0\n",
      "x_max = 8.0\n",
      "\n",
      "# ilosc wartosci wlasnych i wektorow wlasnych, ktore chcemy wyznaczyc:\n",
      "N_eigvals = 4\n",
      "\n",
      "# wybor potencjalu:\n",
      "potential = Konwent\n",
      "# opcjonalne argumenty wybranego potencjalu:\n",
      "args_potential = ()\n",
      "\n",
      "# wybor parametru rho (odpowiedni dla danego potencjalu):\n",
      "#rho = rho_Konwent\n",
      "rho = rho_Konwent\n",
      "# opcjonalne argumety wejsciowe funkcji zwracajacej wartosc bezwymiarowej zmiennej rho\n",
      "args_rho = ()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 3
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def EigenvalEigenvecProblem5(N, x_min, x_max, N_eigvals, potential, *args_potential):\n",
      "    \n",
      "    \"\"\"\n",
      "    funkcja 'EigenvalEigenvecProblem5' rozwiazuje algebraiczne zagadnienie wlasne \n",
      "    wykorzystujac pieciopunktowa metode centralnych roznic skonczonych do przyblizenia \n",
      "    drugiej pochodnej.\n",
      "    \"\"\"\n",
      "    \n",
      "    # dyskretna siatka polozen, gdzie N - ilosc punktow siatki:\n",
      "    x = np.linspace(x_min, x_max, N)\n",
      "    \n",
      "    # krok dyskretnej siatki:\n",
      "    dx = (x_max - x_min) / (N - 1)\n",
      "    \n",
      "    # elementy na glownej diagonali macierzy pentadiagonalnej:\n",
      "    diagonal = 30.0 * np.ones(N) + 12.0 * dx * dx * rho(*args_rho) * potential(x, *args_potential)\n",
      "    # elementy na pierwszych diagonalach macierzy pentadiagonalnej:\n",
      "    diag_edge1 = -16.0 * np.ones(N - 1)\n",
      "    # elementy na drugich diagonalach macierzy pentadiagonalnej:\n",
      "    diag_edge2 = 1.0 * np.ones(N - 2)\n",
      "    # tablica niezerowych element\u00f3w macierzy pentadiagonalnej:\n",
      "    pentadiagonal = np.array([diag_edge2, diag_edge1, diagonal, diag_edge1, diag_edge2])\n",
      "    \n",
      "    # numery diagonali, gdzie 0 oznacza diagonale glowna, \n",
      "    # -1 -pierwsza diagonale dolna, 1 -pierwsza diagonale gorna,\n",
      "    # -2 -druga diagonale dolna, 2 - druga diagonale gorna:\n",
      "    offsets = [-2, -1, 0, 1, 2]\n",
      "    # macierz trojdiagonalna (hamiltonian) zapisana w postaci macierzy rzadkiej:\n",
      "    hamilton = sp.diags(pentadiagonal, offsets)\n",
      "        \n",
      "    start = time()\n",
      "    \n",
      "    # wyznaczenie N_eigvals wartosci wlasnych i odpowiadajacych im wektorow wlasnych\n",
      "    eigvals, eigvecs = alg.eigsh(hamilton, k = N_eigvals, which = \"SM\", tol = 1.0E-4)\n",
      "    # argument \"SM\" oznacza, \u017ce wyznaczone zostanie N_eigvals najmniejszych wartosci\n",
      "    # wlasnych i odpowiadajacych im wektorow wlasnych, a argument \"tol\" oznacza wzgledna \n",
      "    # dokladnosc, z jaka wyznaczone zostana wartosci wlasne\n",
      "    \n",
      "    # !UWAGA! Argument 'eigvecs' stanowi macierz o 'N' wierszach i 'k' kolumnach,\n",
      "    # wiec i-ty wektor wlasny ma 'i' kolumn o dlugosci 'N'.\n",
      "    \n",
      "    #print \"'alg.eigsh(...)' time: %.2fs\" % (time() - start)\n",
      "    \n",
      "    eigvals = eigvals / (12.0 * dx * dx * rho(*args_rho))\n",
      "    \n",
      "    return eigvals, eigvecs"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 4
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "eigvals_a, eigvecs_a = EigenvalEigenvecProblem5(N, x_min, x_max, N_eigvals, potential, *args_potential)\n",
      "print eigvals_a"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "[ 0.55525591  0.55565556  1.00049964  1.11047154]\n"
       ]
      }
     ],
     "prompt_number": 5
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# DYSKUSJA BLEDOW\n",
      "N = 1500\n",
      "eigvals_a, eigvecs_a = EigenvalEigenvecProblem5(N, x_min, x_max, N_eigvals, potential, *args_potential)\n",
      "\n",
      "N_max = 1000\n",
      "\n",
      "N_list = range(100, N_max + 50, 50)\n",
      "measures = 5\n",
      "\n",
      "time_list = []\n",
      "digits_list = []\n",
      "\n",
      "for N in N_list:\n",
      "    eigvals_num, eigvecs_num = EigenvalEigenvecProblem5(N, x_min, x_max, N_eigvals, potential, *args_potential)\n",
      "    \n",
      "    time_start = time()\n",
      "    for m in xrange(measures):\n",
      "        EigenvalEigenvecProblem5(N, x_min, x_max, N_eigvals, potential, *args_potential)\n",
      "    exec_time = (time() - time_start) / measures\n",
      "    \n",
      "    time_list.append( exec_time )\n",
      "    digits = [-math.log10( abs( (e_num - e_a) / e_a ) )\n",
      "                  for e_num, e_a in zip(eigvals_num, eigvals_a) ]\n",
      "    digits_list.append(digits)\n",
      "    \n",
      "    print \"%d/%d/%.2f\" % (N, N_max,exec_time)\n",
      "    \n",
      "for idx in xrange(N_eigvals):\n",
      "    \n",
      "    digit_data = [digit[idx] for digit in digits_list]\n",
      "    pl.plot(N_list, digit_data, \".-\", label = \"$\\widetilde{E}_{%d}$\" % (idx+1))\n",
      "    \n",
      "pl.grid()\n",
      "pl.legend(loc = \"lower right\")\n",
      "pl.xlabel(\"$N$\", {\"fontsize\": \"xx-large\"})\n",
      "pl.ylabel(\"$l_n$\", {\"fontsize\": \"xx-large\", \"rotation\": \"horizontal\"})\n",
      "pl.savefig(\"konwent_num_l_N.png\")\n",
      "pl.show()\n",
      "\n",
      "for idx in xrange(N_eigvals):\n",
      "    \n",
      "    digit_data = [digit[idx] for digit in digits_list]\n",
      "    pl.plot(time_list, digit_data, \".-\", label = \"$\\widetilde{E}_{%d}$\" % (idx+1))\n",
      "\n",
      "pl.grid()\n",
      "pl.legend(loc = \"lower right\")\n",
      "#pl.legend(bbox_to_anchor=(1.16, 0.7))    \n",
      "pl.xlabel(\"$t$\", {\"fontsize\": \"xx-large\"})\n",
      "pl.ylabel(\"$l_n$\", {\"fontsize\": \"xx-large\", \"rotation\": \"horizontal\"})\n",
      "pl.savefig(\"konwent_num_l_t.png\")\n",
      "pl.show()\n",
      "\n",
      "pl.grid()\n",
      "pl.plot(N_list, [t**0.33 for t in time_list], \".-\") \n",
      "pl.xlabel(\"$N$\", {\"fontsize\": \"xx-large\"})\n",
      "pl.ylabel(\"$t^3$\", {\"fontsize\": \"xx-large\", \"rotation\": \"horizontal\"})\n",
      "pl.savefig(\"konwent_num_t_N.png\")\n",
      "pl.show()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "100/1000/0.14\n",
        "150/1000/0.21"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "200/1000/0.41"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "250/1000/0.50"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "300/1000/0.75"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "350/1000/1.00"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "400/1000/1.11"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "450/1000/1.61"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "500/1000/1.76"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "550/1000/2.25"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "600/1000/3.02"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "650/1000/3.35"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "700/1000/4.59"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "750/1000/6.33"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "800/1000/5.44"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "850/1000/6.98"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "900/1000/8.29"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "950/1000/9.24"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "1000/1000/11.46"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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ZLM7ZwkKWXrjA4nPnyC4tZZSnJ1sDAqhnZWWUdZiu3O9B98qP/Bkdz9KYVcSV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\nUW3y8vKYOnUqnp6e1K9fn2nTpnHq1Ck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0dLSMjo7KzMyMpKWlSU1NjdJMt27dktzcXPfP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\n",
       "text": [
        "<matplotlib.figure.Figure at 0xa2ebfec>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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1+bp1lywKHTl3qQl/FxeO1NZaisCW8nLC3d2ZrNfzu4gIvhgxAn8rtYPymvZT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\njz4uKqJFUZgXGnrW+08t/ZY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/3rx5DBw4EADF2xsXwN9NPapo63u2rejoaK/ffvttEhIS\n7CYeya/zr9v33O0hHsnv/Nf9SUpKCsuXLwewjJddZTfto4KCAsLCwjh9+jRTp07l3Xff5brrrgPO\nPwQ6UF3N1Zu/57q0dNY9+7StQraalJQUTf8Bazk/LecGjp+ftI8cuH0UFhYGQHBwMHfcccdFJ5rL\nmpqgsY4gL8e/mhm0v0ej5fy0nBtoPz9xPrsoCrW1tVRVVQHq1Xzr169n1KhRHX6+rLkZc0M1Rj9t\nFAUhhLAXdlEUioqKuO6660hISODKK6/klltuYdq0aRf8bFJGBs9kZ9OgD8LfoI0lLtr3bbVIy/lp\nOTfQfn7ifHYx0Txo0CD279/fqc9m1tWRWVcHXv586+nKc70cmxBC9Cd2M9F8Me0nS2akpbG2rAxq\nilkbfTk3jhps4+iEEPZKJpodeKK5s5KHD2dWcDD8+BgjwwJtHY4QQmiKwxUFvasrywbHgtNpwgP8\nbB2OVWi9b6vl/LScG2g/P3E+hysKADlF5Tg1GHB2drJ1KEII0W21tbUsXLgQo9FIWFgYTz/9NHl5\neZSUlPDJJ5/w7LPP9nlMDlkUcovLcG3SzumoWj8XXMv5aTk30H5+tjZ//nyuv/56cnJySElJoaqq\nijFjxjB+/HgKCgp46aWX+jwmh5toBljy7X95YsN8qt7aacOohBD2Tiaa+8FEM0C+yYQn2jlS0Hrf\nVsv5aTk30H5+9iI1NZWbb76ZCRMm8P7777N06VJef/11Bg8ezPHjx/s0Fru4TqGrCivK8HHRTlEQ\nQvRv48aNw9fXlzlz5jB37lzL+z4+PoSHh/dpLA7XPopfkES2eTNmp0aOLTjAAKPextEJIeyVI7WP\nwsPDSUtLIygoiJUrVzJ37lwyMzOJjY295M9as33kcEcKhU2ZNBmOAnDtq0nkvbnKxhEJIRxRUkYG\nmXV1eDk7kzx8OHrXrg+H1tgGQHp6Ojqdji+++ILU1FQCA9VrsDpTEKzN4YqCDi8APMsT2L5wiY2j\nsQ5HX574UrScn5ZzA23nl1lXx5bycgAM27f3eHtJGRmsGjGiWz+7efNm7rrrLh5++GGys7PJysoC\nID8/v8/bRw5XFPY8ncy1ryaxfeESaR0JIbrNy1k9z2a8ry/rx4zp1l5+27I74319WRIX1+1YUlJS\nmD17NgARERFER0dTWlrKnj17uO2223jiiSd44403ur39rnC4OQUhhOisi40d5c3NJGVksCQurttt\nH2tsQ1EUQkJCOHjwIKGhoZb3//jHP/L888+Tm5tLUlISmzZt6nAb/XpOQQghrEHv6trtdo+1tpGW\nlkZycjL19fWsWbMGUO8ps3btWkaNGoVOp+PEiRNER0f3KM6ukCMFO6Dlvi1oOz8t5waOn5+jjx07\nd+5k5MiR/O53v2PZsmUdfq7fX7wmhBD9QU5ODps2bSI3N5fNmzf3ye+UIwUhhGZpYezIzs7m3nvv\n5dlnn+Wmm2664GeseaQgRUEIoVn9ZeyQ9pHGaH19GS3np+XcQPv5ifNJURBCCGEh7SMhhGb1l7FD\n2kdCCCF6hRQFO6D1vq2W89NybqD9/MT5pCgIIYSwkDkFIYRm9ZexQ9Y+EkKITjAYDDg5Odk6jF5n\nMBisti1pH9kBrfdttZyflnMDx8+vrKwMRVE6fGzevPmi33eUR1lZmdX+m0lRsAP79++3dQi9Ssv5\naTk3kPz6I7spCi0tLVx22WXceuuttg6lz5W33v1Jq7Scn5ZzA8mvP7KbovDOO+8wfPjwftH/E0II\ne2UXReHkyZN8++23PPjgg/3iTIFz5eTk2DqEXqXl/LScG0h+/ZFdnJI6a9YsnnnmGSorK3n99df5\n+uuvz/q+HD0IIUT3ONwpqd988w0hISFcdtllHZ7pYAd1Swgh+gWbt4927NjB6tWrGTRoELNnz+b7\n77/n3nvvtXVYQgjRL9lF+6jNli1bLtg+EkII0TdsfqRwLpk/EEII27GronDDDTewevXqs95bt24d\n8fHxxMTE8Oqrr9oost6Rl5fHxIkTGTFiBCNHjuQvf/mLrUPqFVq9BqW8vJyZM2cybNgwhg8fzs6d\nO20dklW98sorjBgxglGjRjFnzhwaGhpsHVKPPPDAAxiNRkaNGmV5r6ysjKlTpxIbG8u0adMc+rqF\nC+W3YMEChg0bxpgxY7jzzjupqKi45Hbsqiicq6Wlhd/+9resW7eOQ4cO8cknn3D48GFbh2U1Op2O\nt956i/T0dHbu3Mlf//pXTeXXRqvXoDz22GPMmDGDw4cPk5aWxrBhw2wdktXk5OTwz3/+k71793Lw\n4EFaWlr49NNPbR1Wj9x///2sW7furPcWLVrE1KlTyczMZPLkySxatMhG0fXchfKbNm0a6enpHDhw\ngNjYWF555ZVLbseui8KuXbsYOnQoAwcORKfTcffdd/PVV1/ZOiyrCQ0NJSEhAQAfHx+GDRtGfn6+\njfuHwP4AAASCSURBVKOyLq1eg1JRUcG2bdt44IEHAHB1dcXf39/GUVmPn58fOp2O2tpampubqa2t\nJSIiwtZh9ch111133sJxq1ev5r777gPgvvvu4z//+Y8tQrOKC+U3depUnJ3VYf7KK6/k5MmTl9yO\nXReFU6dOERUVZXkdGRnJqVOnbBhR78nJyWHfvn1ceeWVtg7FqubPn89rr71m+cPUiuPHjxMcHMz9\n99/P2LFjeeihh6itrbV1WFYTEBDAE088QXR0NOHh4ej1eqZMmWLrsKyuqKgIo9EIgNFopKioyMYR\n9Z4PPviAGTNmXPJzdv1/qtbaDR2prq5m5syZvPPOO/j4+Ng6HKtpfw2Klo4SAJqbm9m7dy+/+c1v\n2Lt3L97e3g7dejjXsWPHePvtt8nJySE/P5/q6mpWrlxp67B6lZOTk2bHnD//+c+4ubkxZ86cS37W\nrotCREQEeXl5ltd5eXlERkbaMCLra2pq4q677uKXv/wlt99+u63DsSotX4MSGRlJZGQk48ePB2Dm\nzJns3bvXxlFZz549e7j66qsJDAzE1dWVO++8kx07dtg6LKszGo0UFhYCUFBQQEhIiI0jsr7ly5fz\n7bffdrqo23VRuPzyy8nKyiInJ4fGxkY+++wzbrvtNluHZTWKovCrX/2K4cOH8/jjj9s6HKt7+eWX\nycvL4/jx43z66adMmjSJDz/80NZhWUVoaChRUVFkZmYCsHHjRkaMGGHjqKwnPj6enTt3UldXh6Io\nbNy4keHDh9s6LKu77bbbWLFiBQArVqzQ3I7ZunXreO211/jqq6/w8PDo3A8pdu7bb79VYmNjlSFD\nhigvv/yyrcOxqm3btilOTk7KmDFjlISEBCUhIUFZu3atrcPqFSkpKcqtt95q6zCsav/+/crll1+u\njB49WrnjjjuU8vJyW4dkVa+++qoyfPhwZeTIkcq9996rNDY22jqkHrn77ruVsLAwRafTKZGRkcoH\nH3yglJaWKpMnT1ZiYmKUqVOnKiaTydZhdtu5+b3//vvK0KFDlejoaMv48sgjj1xyO3Z1RbMQQgjb\nsuv2kRBCiL4lRUEIIYSFFAUhhBAWUhSEEEJYSFEQQghhIUVBCCGEhRQFIXpo69atHDlyxNZhCGEV\nUhSE6KH777+fPXv22DoMIaxCLl4Togfy8/OJjIwkJyeH6OhoW4cjRI/JkYIQPbB9+3aioqKkIAjN\nkCMFIbph9erVfP7552zfvh0PDw8uv/xyrr76ah555BFbhyZEj0hREKIHLrvsMn7zm9/w0EMP2ToU\nIaxC2kdCdFNlZSUHDx7k2muvtXUoQliNFAUhumnHjh3o9XqGDRtm61CEsBopCkJ007Zt2+QoQWiO\nFAUhuumHH37guuuuA+DQoUN8+eWXNo5IiJ6ToiBEN5WUlDBs2DDMZjMrVqzQ1K1iRf8lZx8J0U0r\nVqxg/fr1DBw4kKSkJAYMGGDrkIToMSkKQgghLKR9JIQQwkKKghBCCAspCkIIISykKAghhLCQoiCE\nEMJCioIQQggLKQpCCCEspCgIIYSw+P/t9CTCgtUdIgAAAABJRU5ErkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0xabf1dcc>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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5XbsWqFXLksMSEZmO8zgscOkS8PzzwLVrcjZ45cqqExER6YE9jts4cwbo1g2o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\n",
       "text": [
        "<matplotlib.figure.Figure at 0xa2dcd8c>"
       ]
      }
     ],
     "prompt_number": 6
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# DYSKUSJA BLEDOW:\n",
      "\n",
      "eigvals_a, eigvecs_a = EigenvalEigenvecProblem5(N, x_min, x_max, N_eigvals, potential, *args_potential)\n",
      "\n",
      "print eigvals_a\n",
      "\n",
      "N_max = 1000\n",
      "N_list = range(100, N_max + 25, 25)\n",
      "measures = 5\n",
      "\n",
      "time_list = []\n",
      "digits_list = []\n",
      "\n",
      "for N in N_list:\n",
      "    eigvals_num, eigvecs_num = EigenvalEigenvecProblem5(N, x_min, x_max, N_eigvals, potential, *args_potential)\n",
      "    \n",
      "    time_start = time()\n",
      "    for m in xrange(measures):\n",
      "        EigenvalEigenvecProblem5(N, x_min, x_max, N_eigvals, potential, *args_potential)\n",
      "    exec_time = (time() - time_start) / measures\n",
      "    \n",
      "    time_list.append( exec_time )\n",
      "    digits = [-math.log10( abs( (e_num - e_a) / e_a ) )\n",
      "                  for e_num, e_a in zip(eigvals_num, eigvals_a) ]\n",
      "    digits_list.append(digits)\n",
      "    \n",
      "for idx in xrange(N_eigvals):\n",
      "    \n",
      "    digit_data = [digit[idx] for digit in digits_list]\n",
      "    pl.plot(N_list, digit_data, \".-\", label = \"$\\widetilde{E}_{%d}$\" % idx)\n",
      "    \n",
      "pl.legend(bbox_to_anchor=(1.16, 0.7))\n",
      "pl.xlabel(\"$N_{}^2$\", {\"fontsize\": \"xx-large\"})\n",
      "pl.ylabel(\"$l_n$\", {\"fontsize\": \"xx-large\", \"rotation\": \"horizontal\"})\n",
      "pl.xlim(None,N_max)\n",
      "pl.xlim(50,1000)\n",
      "pl.savefig(\"konwent_num_l_N2.png\")\n",
      "pl.show()\n",
      "\n",
      "for idx in xrange(N_eigvals):\n",
      "    \n",
      "    digit_data = [digit[idx] for digit in digits_list]\n",
      "    pl.plot(time_list, digit_data, \".-\", label = \"$\\widetilde{E}_{%d}$\" % idx)\n",
      "    \n",
      "pl.legend(bbox_to_anchor=(1.16, 0.7))\n",
      "pl.xlabel(\"$t \\, [s]$\", {\"fontsize\": \"xx-large\"})\n",
      "pl.ylabel(\"$l_n$\", {\"fontsize\": \"xx-large\", \"rotation\": \"horizontal\"})\n",
      "pl.savefig(\"konwent_num_l_t.png\")\n",
      "pl.show()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "[ 0.55525591  0.55565556  1.00049964  1.11047154]\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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w96g+ThLdCn1xc2vcsHBjz09MTCQ2NpaSkhLWrl0LQGFhIevWrSM8PJy0tDT8\n/f2xsrK65WaTtZHgJZpHVfqmI0fU32+7TZ323kS5/G4mtbiYrzMz2XXlCgDt7ezY1qMHgXoMnjmX\ndbyzfD3Lk5aR7/FHl+D2mM30CTbMGJ4QzaVr16507dqVefPmXfP8Sy+9BMALL7yA5dXlJI2ZMSvp\noUTTUhS1A713b3VbElA709eta7bApausZOXFi9yVmEjU/v0UVVYS3707Y7y92d+rV4MDV8jUGNwm\nR+M9eQRHU3N56z9xdHhpEt7z/fn29FyGhd7G1keSaJU3hpNTD0jgEgLo3Lkz2dnZlJSU4OLi0uDr\nyJiXaBqKou6XNWsW5OfDP/4BgwbBc881+RqtqvEsDRDp7ExsdjZB9vZMCghgtJcX9npaROw2Obp6\n4TA6O5xKQxgeMI6/P/Aw3dq11ct7CHE9U68Pc3JyWLRoEa6urkRERNC3b98bHifpoUTzqLk45C9/\ngffeU8e0Zs+GsWObLedgpaLQfd8+Dl/NfNHJ3p5V4eGE6nEiyPpdacxZvZRtzAHbQiwK/Ym9fyUP\n9+9T+8lCNFJLqQ8leInmER39x+ISJyf4/HMYN05ds9UMtOXlfJuVxb/Pnye7rIz8igoinZzY2Igp\n7jVnCv730S/4csMm1qZ/R7HLIbpaP8QTvUfx4ebFMktQNKuWUh9K8BJN7/hxGDgQLlxQ12ft3Qte\nXk3yVtdv7pheWsq/z59n+YUL3O3hwYuBgXRxcGBSSkqjM1+4TR5InvtW9ZcKK9qU3sMzvR7jtfvv\nwcFGv9uZCFFXLaU+lOAlmk5Wltot+NNP8NJLcOgQfP11k45n1dzc0dvaGiuNhkkBAcT4++OvhxmD\nigI/bk5h7rrFHLL7GKxLsSpow9aJm+nbOajR1xeisVpKfSjrvIT+5efDhx+quxY/9RQkJ4OHR+3n\nNdKV8nIulJUB4GhhwbsdOvDY1cXE9XV9/rZLV/J5Y+mP/HJ+EWVOJ+nr+ihLB25h2qqPpVtQCCMk\nLS9Ru6qa3s4Ohg6FDz6AIUPg7bebJY3TuZIS/nn+PIszMxng6kp+RQUrwsMb1SXoH6OOZ2FZgl1x\nEKVt19K6YiDP3fY0r44cgY2V/jeOFEIfWkp9KC0v0Xg1M30eOKCu0erZU+9vc/141omiIj5KT+f/\ncnN50s+PhF69aGfX+LGmPUkXueSyCZxPA+BhWczWZ48T5OtXy5lCCGMhwUvcWnIyJCWpPwcHw65d\njU9VfRMKEc3vAAAgAElEQVQpxcXV41mddu3C3tKSl1u14ovgYFwbuaC5rExh7rI4vti7kAsu63Bw\ncKIc6OETxean1uNmJ92CQpgSCV7ixvLz1W7BxYth8mQ4eBC++qrJJmPoKivJ1ekAcLCwYH5QEI/7\n+WHVgPQxNae4L3roUz75bRXxhQuxtbLmodBJzBv/GfZ2GmLWxLBw5EIJXEKYoDqPee3YsYNPP/2U\nvn378vLLLzd1ua7RUvp4jYKiwNKlMG2aOr41bx74NV13WlFFBV9nZvJBWhrtr3YJrgoPx9264WNO\n12S+qLCiS8V4/nZXDONu7ye7DwuT11LqQ72MeaWmpjJ//nx++eUX7r77br0VThiBmtPupk+HN96A\nkhJYsQJukralwW9VY0zrs06d+P7CBT5NT6e/qysrwsLo3Yg8ZwDnMouYsiiWPIf9AFgWtGHHs3GS\nU1AIM1Tnltf58+dp3bo1qamptG3bvHnbWso3DYOomRnD1lad/v70002SGaPmGi1rjYbxvr5Ma92a\nLo1M3fTz1tPMXPU5R62/pRX9eDbqSRbujGX7tK9kirswOy2lPtTbbMO4uDjatm3b7IFLNCFFUXee\nA/Dxgd27m2zqe3ZZGWeLi9W3srZmY7duRDg51fs6VeNZVtgzpv2zLE9ZzBXnXdzu8RR7x+8hsoPa\nyvr7Qw/otfxCiLopKirirbfeYvHixVhYWPDkk0/y/PPPY29vz4YNGzhy5AjvvPNOo9+nzqs74+Li\nGDRoUKPfUBiJs2fhnnugrAwGD1ZnFTZB4MrR6Zhx+jShe/YwzMODkR4eJPfp06DABermjnnu8eS4\n/8aX2U8zoecotLPPEv+396oDlxDCcKZMmcKAAQM4c+YMcXFx5Ofn061bN6KiosjMzGTOnDl6eZ86\ndxt26tSJWbNm8dhjj+nljWtKTk7mkUceqf799OnTvP3229Wbl7WUZnKzqKhQuwbnzIFXXoHXXgMb\nG72/TV55OR+np/Ov8+cZ7eXF39q2pXUj1mhtO5DJy0v/xQH798FKh82VEJKn7qSdX9NM2xfCWLWU\n+lAvuQ2rxrvOnTtHq1at9FrA61VWVhIYGMiePXto3bq1WsgW8sdqcocOwbPPgqMjfPmlum5LT6om\nY9hoNPR1ceHzjAxGeHoyq21bOtjbN+iaigLf/JLIP9Z/xHmn1UTZTmD6XU/x0g/zJGWTaLFMpT5M\nSEhg1qxZ5ObmMnHiRBRFQavV8tlnn7Fp0ybat791T4lexrzi4uLo0KFDkwcugI0bNxIUFFQduEQj\nVM0ktLWF0FB1Cvy776oTMvQ8ZTy5qIiteXkAHC8qYmuPHoQ4ONTrGjXHs0a3e4ZlJ76k2Oko97Z/\nkV1PniTwav7EB277Qa9lF0LoX2RkJM7OzowfP54JEyZUP+/k5ERAQECjr1/n4NVc413Lly9n/Pjx\nf3p+9uzZ1T9HR0cTHR3dLOUxaTXTOh09ComJel+zVako/PfCBfbm5wMQ5uDA9p49G5R3MFOXzJWr\nW5AsvPA7U3r/k7njH8HOWv/dmkKIprd161b+9a9/AbB06VImTJjA4MGDsdXDDhB1qmHi4+N58803\nG/1mtSkrK2PNmjXMnz//T6/VDF6iDnQ6SE9Xf+7YUd1jS8/ZMTZfvszrp09jAfwQFsZ/srIatIdW\n5sUSYj5fzBWnvQDYXAkmeeouGc8SogFi1sSQkpOCg7UDsaNj651BprHnV0lKSsLa2poVK1aQkJCA\np6cnAMF6Gq6otZY5f/48J0+eJDo6muXLlzNs2DA8mmj7i3Xr1hEZGYm3t3eTXL/FOHECHn1UnT0Y\nGgr/+Y9eA9fhggKmnT5NclER73bowBhvbzQaDfde/Y+zrk6ey+fZL78gvuxjWln04p8DVvHepq9l\nPEuIRkjJSSH+rNrj4j6/cV8AY9bE8MOYhnXTb9myhdGjR/Pcc89x+vRpTpw4AUBGRkbzdBtmZGTg\n6+tLYGAgR44cuWZWoL4tW7aMcePGNdn1zZ6iwDffwIwZMGsWvPiiXsa2qiZjaIAAGxs2Xr7MzLZt\nWRUeXq+9tKrGtDSKFa0tIzlivYiOFkP5dfxv3NWjKwB/vWdYo8srREvmYK2ONUcFRLH+sfonnR6x\ndATrTq4jKiCKhSMXNrgccXFx1fV5YGAgbdq0IScnh40bN+Lk5ERycjIzZsxo8PVrnW1YUVHB2LFj\n6dixI0OGDGHo0KGkpKSwbds2Dhw4wNChQykvL+fHH39k+fLlDS5IYWEhbdu2JTU1FWdn52sLaSKz\nawzq0iV1JmFqqjoxIyxMb5cecOAA265Oxgixt2dXZGSDsrw7T+5PgftOAKzy27MtZj23BXfUWzmF\naAlqqw+1JdpGJZ1u7PkAiqLg4+PD4cOH8asxzv63v/2NN998k4yMDL799ttbDkc1erahpaUlP/30\n0zXPnTp1ir59+/LVV19VD8a9/fbbFBYW4tjAVD+Ojo5cunSpQee2WFWzCYuKIC1N7SpcvlydXagH\niqLww8WL7L1yBYBujo7E9ehR78CVcOwST339HgXO6piWnbYbx6fHSdegEE3Azc6twV19+jg/MTGR\n2NhYSkpKWLt2LaA2TtatW0dERATW1tZ6aYw0aEuUu+++mwULFvDoo48CkJ6ejr29fYMDl2ig5GTY\nqs7OY+BAeP99vV36cEEBL508Sa5Ox4rwcJY0YDJG4olcnvzyQw5afUGk0yP836gDPPPdP9g+Xca0\nhDBXXbt2pWvXrsybN++a56uSTgB62d2hwft5bdy4kQ8//BCA7777jokTJ7J69Wruu+++RhdK1EFq\nqrrHFkCPHrBqlV4uqy0vZ1ZqKssvXODNdu2YFBCAlUbDPbVMxqi5h1bshM+Z+eMi9ln8m672D7L/\n6f10b6/mxEzrIWu0hGjpDNbyAtBqtdVTHh0cHCgpKcFOD1u0izpYvVod35o+HQ4cgIULGzybsGoy\nhr1Gw92ensw9d477PT052rs3XvXYUytLl1K9h9awn4MJt5nA7if3ENWxQ4PKJYQwTwUFBfz0008k\nJCRw5MgRwsPDG3SdOuc2NCSZsHGVTqfut/XDD+rYlh7226q5TYmHlRXru3Uj8roJM7XJ0Zbh/4/u\n6NyOoSn24Mf71zO6b2SjyyaE+LOWUh/qbUsUYWDp6fDII+DiAgkJ4OXV6EsWVVRwrqQEgPZ2duyL\njMSjHq2tsjKF5//9I9+mzcDTsgOVea3ZN+2/Mp4lhGhy0vIyBevXwxNPwEsvwbRpUI+1VTezITeX\nSSkpRDo5UaYoLOnSpc6TMRQF5nwXz9y9r2NtW877w95n0rDBjS6TEKJ2LaU+lJaXqaqaBp+eDoWF\nsGyZuutxI+XodLx66hRxWi2fd+rE3XXIilFzMsYb/f/O23FzKXA8wqu3zWXOuIex1EMwFUKI+pDg\nZayOHYPt29WfR45sdOBSFIX/XrzIlJMnGevtzZGoKJwsLet0bs3JGK8c2sS4kHl8HbMCBz2tJxNC\niPqS4GWMzp//Yxp8r15qbsIGqJnWyUaj4XxZGSvDw7nNxaXO18jRllGoyQLAotCPnRN/p09wuwaV\nRwgh9EWCl7E5cgTuuQdefVXdxqQR0+BTioqIv5rWKczBgf29etU5F6GiwLSvfuOjYy/jbdWOyrwO\n7JkWK5MxhBBGQYKXMYmLg7Fj4eOPocbmbQ1xsayM40VFwB97bNU1cK3Zfponl02h0OEo86I/4bX7\n72lUWYQQQt8keBmLZcvg5ZfV9VuDGzdzb11ODhOTkxnr40NGaSlfh4TcdCZhzckYqyd+zYtLPueA\n5efcH/QqS1/4Qca1hBBGSYKXoSkKfPABfPopbNoEERENvlRRRQVTT53il5wcloaGEl2H7saakzH6\nLetIJ6v7SfzLQcLbtGpwOYQQoqlJ8DKEqmnw9vbQpg3s3Kk+WjU8YCTk5zPh2DEinZw4FBVVjzVb\nVxNk6uyZ3+tHXn9AugiFEMZPgpchpKRAvNrawdtb3fnY1bXel4lJTialqIjMsjJydDr+FRzMIz4+\ndTq3sKiCUfP+yRX7Q9hdieDQlE0Et5IdrIUQpkFWlxqCjY36r4eHOruwAYEL4HBhIfF5eaQUF3Ob\ni0udA9fiXxPxmt6Xg8Wr2fbEboo/TJTAJYTQi6KiIqZPn46vry/+/v7MmDGDtLQ0Ll26xLJly5g5\nc6Ze3keCV3O7ckV9tG+vtrjqGHCut/nyZfbn5wPQy8mJ70NDaz0nO6eEnq/NZOLWO3mqawwX3tvM\n7V06Nej9hRDiRqZMmcKAAQM4c+YMcXFx5Ofn061bN6KiosjMzGTOnDl6eR/Jbdic8vLgrrvU/bf+\n9a8G5ShUFIX30tL4JD2dL4KDWZqdfdNNImvOJHwi9AUWHHuF1rYR/PrXTwkJ9NfHJxJCNDOzqQ9r\nUdvnlODVXC5fhuHD4bbbYMECaMBOonnl5Txx/DhZZWWsCAujVS3T2N0mR1fPJERnx5wey5g5elRD\nSi+EMBKmUh8mJCQwa9YscnNzmThxIoqioNVq+eyzz9i0aRPt27e/5fmSmNcY5ObC0KEwcCB8+GGD\nAldiQQGjk5IY7uHBD6GhdVpwXK6o251oir3Y80wCvTq1qff7CiFEQ0RGRuLs7Mz48eOZUCPpgpOT\nEwEBAY2+vox5NbVLl9RFx3fe2eDA9V1WFnceOsTsdu34V6dOtQauy1fK6PnaTIrsUnHR9id1ygkJ\nXEKIZrd161aGDx8OwNKlSwEYPHgwtnpIfiAtr6Z04QIMGaJmhZ8zp16BKyY5meSiIlJLSrDWaNjc\nrRsRTk61nvfjluM8tvJRvOx8Of7yIYID/BrzCYQQpqZqHamDA8TG1j83amPPvyopKQlra2tWrFhB\nQkICnle3XwoODm7Q9a4nwUvfqv7wlpZqdviHH4bZs+vd4koqLGTnlSsAjPLyqjVw6XQKD777OWuL\n3uSZsLdZGDMJTQNaeUIIE1dzHam7e+OuFRMDP/zQoFO3bNnC6NGjee655zh9+jQnTpwAICMjQy/d\nhhK89K3mfzhhYfCPf9T7EseLijhQUABAlJMTi0NCbnhc1WxCjWJJZYUF2GmJe2o7A8I6N7j4QggT\n5+Cg/hsVpe7CXt+W04gRsG6dev7ChQ0uRlxcHOPGjQMgMDCQNm3akJOTw4oVK2jdujWJiYmMHDmS\nnj17Nuj6Mualb1ULkAMC/thMsh7itVoGHjjA+x06MMbbm/Xdu9801VNVXkKtx2ZKbc9z4d2dEriE\naOliY2HMmIYFLn2cj7qkJz4+nv79+wNga2uLlZUVH330EaWlpQQGBvLKK6/wwQcfNOj6IC0v/dLp\n1EeHDrBvX73/8Euzs5ly8iSxoaEMcXfnhVvkOszL11FgeRYAmyshJL++E1tr60YVXwhhBtzcGtzV\np4/zExMTiY2NpaSkhLVr1wJQWFjIunXriIiIYOrUqQAcPXq01unytyLrvPRFUeCppyAnB1auhDom\nxlVPVXjn3Dm+yshgbdeuhDs63vL4nYczGbbwYRxtbbGsdOT3ad/KJpFCtBAmUR/WwTvvvMOUKVNw\nqOrmvI4sUm4us2bBb7/Bli1QS/CpSVdZyaSUFA4VFPBLRAT+tUwhfTd2K387MI67fSbx86t/w7IB\nWTqEEKbLJOrDWqxevZpBgwaRlZVFp043TlFnMsFLq9UyceJEkpKS0Gg0LFq0iNtuuw0wgT/W11/D\nvHnqtiZ1yFUYk5xMSnExNhoNZZWVOFlZsTw0FCdLy5ueo9Mp3PXWR8Tp3uPD25cw+d679PkJhBAm\nwujrw1qsXLmSuXPn4ubmRnR09E0T9ZpM8HriiScYOHAgTz/9NOXl5RQWFuJ6Ndu6Uf+xfv0Vnn4a\ntm2Dm3yDuF70wYPEa7UABNnZcbxPH6xuMa39VPoV+s57mhK7s8Q9v4KeHdrqpehCCNNj1PWhHplE\neqi8vDy2bdvGkiVLALCysqoOXEZt3z544glYvbrOgQtQx8eAVra27I2MvGHgqpoGX6lUUGSZSVeP\nIWyb+T2Otnb6Kr0QQpgsowheqampeHt789RTT3Ho0CEiIyNZsGDBNQN5s2fPrv45Ojqa6Ojo5i9o\nTampcN998NVX0LdvnU87UVTEyeJiejo5sakO0+ABnPKi2P/WF3opthBCmAOj6Dbct28fffv2ZefO\nnURFRTF58mRcXFx46623ACNqJldlz7CygrNn4eWX4cUX63x6clFRdY7Cif4335KkvFzB/vXOlLue\nwDYvjORp22U2oRACMKL6sInV9jmNYqpaq1ataNWqFVFRUQA89NBD7N+/38CluoGq7BmbNqnpn+oR\nuI4WFjL44EHmtG9/y8CVl68j6JVnsNHY46sdKYFLCCFuwCi6Df38/GjdujUpKSkEBwezceNGwsLC\nDF2sP6vqxnR3V2cW1tGRwkKGHTrEe0FBPOrre9PjUs5piXr/IVzsHUibtQOPOiTiFUKIlsgoghfA\np59+yoQJEygrKyMoKIjFixcbukh/NmYMbN0KBw+Ch0edTjlUUMBdiYl8FBTEuFsErk37znL39/fQ\nw3MQO/7+CVa3mDYvhBAtnVGMedXGKPp4T51Sd0Fetw569arTKfvz8xlx+DCfduzImFus//pydQLP\nb7uPR9pM5fsXX5Zs8EKImzKK+rAZmMRUeaNXWgpjx8Lf/15r4KpagKyrrCSlqIgvO3fmQW/vmx7/\nyhdr+OTM08yOWsissQ/ou+RCCGGWJHjVxdSp0LYt/PWvtR6aUlxcvQC5v4vLDQNX1RquIs1FKmxy\niL33Fx65o4/eiy2EEOZKgldtVq6ENWtg//66bSh5tZnb0d6eX7p2veEhNddw+WhHSOASQoh6kuB1\nK2fOwKRJavCqw46kl3Q60kpLb7kAubxcIf/qVib22h7smb5U36UWQgizZxTrvIxSWRk8/DBMmwZ9\nam8ZFVdUcN/hw4z18SGhV68bBi6dTiFs6kvYK+74593PsembZQ2XEMKsFBUVMX36dHx9ffH392fG\njBmkpaVx6dIlli1bdtNEvPUlwetmZsxQM8S/8kqth1YoChOOHaODvT3v3GRztTJdJV2mPk+2xT5O\n/H0LGR+tksAlhDA7U6ZMYcCAAZw5c4a4uDjy8/Pp1q0bUVFRZGZmMmfOHL28j0yVv5E1a9TsGfv3\ng6fnLQ9VFIWXT57kSGEhv3Xtis0N9tcqLaskZOoktFbHSJ71Kz6uLk1VciGEmZOp8ioZ86opJgYO\nH4aEBDWA1RK4AD5KT2eLVsu2Hj1uGLiKSyoIeX0iBTanOfnmb3g6S9YMIYT5S0hIYNasWeTm5jJx\n4kQURUGr1fLZZ5+xadMm2t+kl6quJHjVlJICu3apP3/zDQwffsvDl1+4wCfp6ezs0eOGY1xFxRUE\nT3uSUpvznJz9K+5Odd9hWQghTFlkZCTOzs6MHz+eCRMmVD/v5OREQEBAo68v3YY1hYXB0aPqQuQN\nG8Dt5mNS8VotY5KS2NitG11r5CCsWsNlpdhhUemIxjaflLdW4VpjexchhGgoU+o2DAgIIDExES8v\nL5YuXcqECROqc9jWRroN6yorS30MHw7Ll98wcFVlz6hUFI4VFrI8LOyawAXXruGyKPLj8puncXGw\nb5aPIIQQVfWUg4UFsaGhN90zsKnOr5KUlIS1tTUrVqwgISEBz6vDMHUJXHUhwavK1KkwcSLMn3/T\nQ2pmz+jt7MydN1j7Zc3VQFXiSuLzByRwCSGaVc16yn379kZdKyY5mR8auMPHli1bGD16NM899xyn\nT5/mxIkTAGRkZOil21CCF0BcnJotPinplofZX82w4W9jw/916/an1xUF/CxCySnew8GYw4S19WuK\n0gohxE05XJ04FuXszPpu3erdchqRmMi63FyinJ1Z2Llzg8sRFxfHuHHjAAgMDKRNmzbk5OSwYsUK\n/P39OXnyJMOGDSMyMrJB15d1XmVl8Pzz8MknUMv+WT2dnfGysiIxKuqG/0GMnvslKZarOTn5OF07\nNP6bhRBC1FdsaChjvL0bFLj0cT6oS4ji4+Pp378/ALa2tlhZWfHRRx/h7u6Op6cnnTp1IiUlpUHX\nB2l5wccfQ/v2MGrULQ+L12pZlJXFwagovKyt//T6awt/4ecrs9n69HY6+N08i7wQQjQlNyurBnf1\n6eP8xMREYmNjKSkpYe3atQAUFhaybt06IiIieOyxx0hNTWX9+vW89dZbDX6flj3b8OxZiIyEPXug\nQ4ebHnaxrIweCQl83bkzd91gE8rPft7Li7+PYOmItYwb0Fv/5RRCiKtMabbhrezatYvVq1czd+7c\nG75e2+ds2d2GkyfDyy/fMnBVKgqPHz/Oo76+Nwxcv/5+ir/uuJ+3e30jgUsIIWoxbdo0jh49iq2t\nLcnJyQ2+TsvtNvzlF3WCxrJltzzs/bQ0rpSX83a7dn96LfHkJe7/8W6e7DSLmQ/d10QFFUII8zFq\n1ChOnjxJUlKSdBvWW1ERhIfDF1/AsGE3PWxHXh6jk5LY27Mnre3srnktK6eYoH/cSW/fgWyZ+a7+\nyiaEELdgLt2GtZFFyjfy7rsQFXXLwJWj0zH+6FG+7ty5OnBVZ8/AnspyS1o5d2DjjHeaq9RCCCGu\nannBKzkZPv8cDh266SGKovDk8eOM8fHh3hrJeWtmz9AU+XD+H2lY3iAZrxBCiKbVcoJXTIyaePfI\nEXWPrsDAmx76UXo6F3U6frou67E1V/MT6uzY9cxe7G1smrLEQgghbqLlBK+UFIhXW00cOHDDQ2KS\nk9mXn8+RwkL2RUb+aYuTN+54g1cObGLpkHh6B7dp6hILIYS4iZbT51WV1T0kBL766oaHHCsq4kBB\nATpFYc7Zs9e8di6rgNe3T+TlDl8zPlqmxAshhCG1nNmGWi08+6wauG6y1UmHXbtILSn5U06wykqF\ndlOewNnRiqS5ixpXDiGEaASZbahqOd2Gbm7w4483fflIYSF55eXc5+nJki5drsnp9egH33LROoFD\nb+xpjpIKIYSoRcsJXregKAp/SUlhTvv2/OW6iRz/3ZzE8tzX+XV8nOyELIQwOHd3dzRXd7gwZ+43\n2HKqJglewH+ysymprCTmuj1mzl8s5LE1Y3kudD539Wx4okohhNCX3NzcOh9rzl2MLWfM6yZydTpC\n9+7ll4gIejk7Vz+vKNBh8jPYOJRxfO5/WsQ3HSGEeTHn4GU0La927drh4uKCpaUl1tbW7NnTPONL\nM1NTGe3ldU3gAnjyo+/JtN5B+ox9EriEEMLIGE3w0mg0xMXF4XGDzO1NZc+VK6y6dImjUVHXPP9T\n/HG+uziFn8duwsvl1htUCiGEaH5GE7yAZm3eVlydpPFehw64X91cMmRqDJm641xxOMDDfm8xsnfX\nZiuPEEKIujOa4KXRaBgyZAiWlpZMmjSJZ5999prXZ8+eXf1zdHQ00dHRjXq/LzIycLK05FFf3+rn\nsnQpXHHfBsCOc78DUxr1HkII0Zzi4uKIi4szdDGahdFM2MjMzMTf35+LFy8ydOhQPv30U+644w5A\n/4OOWWVlROzdS1z37oQ5/jH93XFyb4rc9+Kg7cnR6Zto63vjxcxCCGEKzHnChtGkh/L39wfA29ub\nBx54oEknbEw9dYqn/fyuCVy5eaWUWuTgou0vgUsIIYycUQSvoqIi8vPzASgsLGT9+vVEREQ0yXvF\nabVs1Wr5+3U7I496/338LMPJ+3i7BC4hhDByRjHmlZ2dzQMPPABAeXk5EyZMYNgtNopsiJjkZJKL\nikjIz+eL4GCcLC2rX/u/PafZXv4xu55N0Ot7CiGEaBpGM+Z1K/rot40+eJB4rRaAMd7e/BCmZsyo\nrFTwnnwv/VrdzprXZzS6rEIIYSzMeczLKFpezcHh6t5cEY6OLOzcufr5V7/6mUKb0/z35ZWGKpoQ\nQoh6Mooxr+YQGxrKGG9vtvboUZ0x/vzFQj498TIfDv43DrayK7IQQpiKFtNteCOR06ZzhTROzF+q\n92sLIYShSbehGfox7igHNF9z+PnDhi6KEEKIemox3YY1lZcrPPO/5xkX8CZhbfwNXRwhhBD11CKD\nV8y/llJpfYXFz//F0EURQgjRAC2u2/BEmpYlGVP5z8hV2Fi1uI8vhBBmocVN2Ojy6otY2+lIfOdL\nvVxPCCGMlUzYMAMhU2M4p9tPsXMi2x45bujiCCGEaIQWM+aVpUuh2D0BrHSM+2a6oYsjhBCiEVpM\n8LLGAQAHbS+2T1to4NIIIYRojBYTvPbNiKVV3hiOTt8gWeOFEMLEtbgJG0II0VKYc93ZYlpeQggh\nzIcELyGEECZHgpcQQgiTI8FLCCGEyZHgJYQQwuRI8BJCCGFyJHgJIYQwORK8hBBCmBwJXkIIIUyO\nBC8hhBAmR4KXEEIIkyPBSwghhMmR4CWEEMLkSPASQghhciR4GUhcXJyhi2CU5L7cnNybG5P70jIZ\nTfCqqKigR48ejBw50tBFaRbyP9yNyX25Obk3Nyb3pWUymuC1YMECQkND0Wg0hi6KEEIII2cUwSs9\nPZ1ff/2ViRMnmu2un0IIIfRHoxhBtBgzZgxvvPEGV65c4YMPPmDNmjXXvC6tMSGEaBgjqOKbhJWh\nC/DLL7/g4+NDjx49btp3ba43XwghRMMYvNtw586drF69mvbt2zNu3Dg2b97M448/buhiCSGEMGJG\n0W1YJT4+/obdhkIIIURNBm95XU/Gt4QQQtTGqILXwIEDWb16taGLoRdpaWkMGjSIsLAwwsPD+ec/\n/wlAbm4uQ4cOJTg4mGHDhqHVaqvPeffdd+nUqRMhISGsX7/eUEVvFtev65P7otJqtTz00EN06dKF\n0NBQdu/eLfcG9XOGhYURERHB+PHjKS0tbbH35emnn8bX15eIiIjq5xpyLxISEoiIiKBTp068/PLL\nzfoZ9EIRTSIzM1M5cOCAoiiKkp+frwQHBytHjx5Vpk6dqsyfP19RFEWZN2+eMm3aNEVRFCUpKUnp\n1jBwrTsAAAbMSURBVK2bUlZWpqSmpipBQUFKRUWFwcrf1D788ENl/PjxysiRIxVFUeS+XPX4448r\n33zzjaIoiqLT6RStVtvi701qaqrSvn17paSkRFEURRk7dqzy7bffttj7snXrVmX//v1KeHh49XP1\nuReVlZWKoihKVFSUsnv3bkVRFOXuu+9W1q1b18yfpHEkeDWT+++/X9mwYYPSuXNnJSsrS1EUNcB1\n7txZURRFmTt3rjJv3rzq44cPH678/vvvBilrU0tLS1PuvPNOZfPmzcq9996rKIoi90VRFK1Wq7Rv\n3/5Pz7f0e5OTk6MEBwcrubm5ik6nU+69915l/fr1Lfq+pKamXhO86nsvMjIylJCQkOrnly1bpkya\nNKmZSq8fRtVtaK7OnDnDgQMH6NOnD9nZ2fj6+gLg6+tLdnY2ABkZGbRq1ar6nFatWnH+/HmDlLep\nTZkyhffffx8Liz/+85P7AqmpqXh7e/PUU0/Rs2dPnn32WQoLC1v8vfHw8ODVV1+lTZs2BAQE4Obm\nxtChQ1v8fampvvfi+ucDAwNN7h5J8GpiBQUFjB49mgULFuDs7HzNaxqN5pYTVMxx8krNdX3KTSa6\ntsT7AlBeXs7+/ft5/vnn2b9/P46OjsybN++aY1rivTl16hSffPIJZ86cISMjg4KCAr7//vtrjmmJ\n9+VmarsX5kKCVxPS6XSMHj2axx57jFGjRgHqt6KsrCwAMjMz8fHxAdRvPmlpadXnpqenExgY2PyF\nbmI3Wtf32GOPtfj7Auq34latWhEVFQXAQw89xP79+/Hz82vR92bfvn3069cPT09PrKysePDBB/n9\n999b/H2pqT7//7Rq1YrAwEDS09Oved7U7pEEryaiKArPPPMMoaGhTJ48ufr5++67jyVLlgCwZMmS\n6qB23333sXz5csrKykhNTeXEiRP07t3bIGVvSnPnziUtLY3U1FSWL1/O4MGD+e6771r8fQHw8/Oj\ndevWpKSkALBx40bCwsIYOXJki743ISEh7Nq1i+LiYhRFYePGjYSGhrb4+1JTff//8fPzw8XFhd27\nd6MoCt999131OSbDsENu5mvbtm2KRqNRunXrpnTv3l3p3r27sm7dOiUnJ0e58847lU6dOilDhw5V\nLl++XH3OO++8owQFBSmdO3dWfvvtNwOWvnnExcVVzzaU+6I6ePCg0qtXL6Vr167KAw88oGi1Wrk3\niqLMnz9fCQ0NVcLDw5XHH39cKSsra7H35ZFHHlH8/f0Va2trpVWrVsqiRYsadC/27dunhIeHK0FB\nQcpf//pXQ3yURjGqDBtCCCFEXUi3oRBCCJMjwUsIIYTJkeAlhBDC5EjwEkIIYXIkeAkhhDA5EryE\nEEKYHCtDF0AIc/Xjjz+SlpbGoUOH6N27Ny+88IKhiySE2ZDgJUQTOHXqFAUFBbzyyiuUlpYSEhJC\njx496Nevn6GLJoRZkG5DIZrA4cOHmTVrFgC2trZERUWxY8cOA5dKCPMhwUuIJnDPPfewbt266t/P\nnz9Ply5dDFgiIcyLBC8havHzzz8zduxYbG1t8fHxobS09JrXp0yZgpeXF05OTtx///2cP38ea2tr\nwsPDATh48CDA/7dz96ypQwEYxx9wqiB1CA4tuFSwm3Xri1DoKEL3DApCCynOGfwGpZOUlmx1dO7o\nUvAVXDq4FF2kH6AgFl3acIfLLQRLlTtE0vx/W85J4NkezuHkqFAo+J4d+K242xBYw9vbm0zTVLPZ\nVL1eV7FY9Mzf3Nzo+PhYJycnnvHFYqFyuazb21sZhuFnZOBXY+UFrKHdbsu2bWWzWd3f3y/Nv76+\nLhWXJF1fX6tWq8kwDE0mEx+SAuFAeQFr6Pf7Ojo6kmVZGgwGen5+XvmN4zjK5/NyXVeTyUT9ft+H\npEA4UF7AGubzuba2tmSapra3t3V3d/c19/Lyov39fc/7nU5HlUpFh4eH2tnZ0d7enpLJpN+xgV+L\n8gJWmE6nisfjkqRoNKpSqaRGo6HpdCpJarVaOj099XyTy+X08fEh13Xluq4+Pz+/3VYE8H8oL2CF\nbrerXC739WxZlubzuR4eHiT9/afr38lCAP6gvIAVer2ep7zS6bTOzs7kOI4kiQO7gP8oL2CF2Wym\naDTqGbu6utJoNJLjOEqlUhtKBoQXdxsCP3h/f1csFlsaPz8/1+7urmzbVqvV2kAyINxYeQE/eHx8\nVCaTWRqPRCK6vLxUJBLRwcHBBpIB4cbKC/jGcDiUbdt6enpSIpHQeDxWtVr1vHNxcaHhcLihhEC4\ncT0UACBw2DYEAAQO5QUACBzKCwAQOJQXACBwKC8AQOBQXgCAwPkDsCtWI5tyuyoAAAAASUVORK5C\nYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0xb4206cc>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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dQ0TkImealtcXsbGU+fvz0KzHPB2KiIg0obS0lFmzZhEeHk6vXr2YPXs22dnZ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\nPXdGE4NQvTV2gKqqKtLT03n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       "text": [
        "<matplotlib.figure.Figure at 0xa927d0c>"
       ]
      }
     ],
     "prompt_number": 9
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# WYKRES WARTOSCI ENERGII DLA KOLEJNYCH POZIOMOW ENERGETYCZNYCH:\n",
      "\n",
      "N_eigvals = 6\n",
      "\n",
      "eigvals, eigvecs = EigenvalEigenvecProblem5(N, x_min, x_max, N_eigvals, potential, *args_potential)\n",
      "\n",
      "print eigvals\n",
      "\n",
      "fig, ax1 = pl.subplots(figsize = (8, 5))\n",
      "ax1.set_yticklabels([])\n",
      "ax1.set_ylabel(\"$\\psi_n$\", {\"fontsize\": \"xx-large\", \"rotation\": \"horizontal\"})\n",
      "\n",
      "ax2 = ax1.twinx()\n",
      "\n",
      "num_x = len(eigvecs)\n",
      "dx = (x_max - x_min) / (num_x - 1) \n",
      "x_list = [x_min + i * dx for i in xrange(num_x)]\n",
      "print len(x_list)\n",
      "h_list = [potential(x_i) for x_i in x_list]\n",
      "ax2.plot(x_list, h_list, color = \"black\")\n",
      "\n",
      "for i in xrange(N_eigvals):\n",
      "    ax2.plot([x_min, x_max], [eigvals[i],eigvals[i]], color = \"orange\")\n",
      "    ax2.plot(x_list, eigvecs[:,i] + eigvals[i], color = \"green\")\n",
      "\n",
      "ax2.set_xticks([x_min, x_max])\n",
      "ax2.set_xticklabels([\"$x_{min}$\", \"$x_{max}$\"])\n",
      "ax2.set_xlim(x_min, x_max)\n",
      "ax2.set_yticks(eigvals[1:])\n",
      "ax2.set_yticklabels([\"$n = 0, \\ n = 1$\"] + [\"$n = %d$\" % i for i in range(2,len(eigvals))])\n",
      "ax2.set_ylim(None, eigvals[-1] + 0.1)\n",
      "\n",
      "pl.savefig(\"konwent_num_all.png\")\n",
      "pl.show()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "[ 0.5552559   0.55565554  1.00049963  1.11047153  1.3263137   1.60634957]\n",
        "550"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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Xs+LoCj7N+BQnayceiX+ETyd1XL4ZyGQybou4jQnhE0gtTGVh2kJe3fMqL6e8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\nAAAAAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0xbc7734c>"
       ]
      }
     ],
     "prompt_number": 19
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# WYKRES FUNKCJI FALOWEJ:\n",
      "\n",
      "x = np.linspace(x_min, x_max, N)\n",
      "eigvals, eigvecs = EigenvalEigenvecProblem5(N, x_min, x_max, N_eigvals, potential, *args_potential)\n",
      "\n",
      "fig, ax1 = pl.subplots(figsize = (8, 5))\n",
      "ax2 = ax1.twinx()\n",
      "\n",
      "for idx in range(N_eigvals)[0:6]:\n",
      "    \n",
      "    psi = 9.0 * eigvecs[:,idx]\n",
      "    ax2.plot(x, psi + eigvals[idx], label = \"$\\psi_{%d}(x)$\" % idx, color = \"red\")\n",
      "    \n",
      "ax1.set_ylabel(\"$\\psi_n(x)$\", {\"fontsize\": \"xx-large\", \"rotation\": \"horizontal\"})\n",
      "ax1.set_yticks([])\n",
      "ax1.set_xticks([])\n",
      "ax1.set_xlabel(\"$x$\", {\"fontsize\": \"xx-large\"})\n",
      "\n",
      "ax2.set_xlim(x_min, x_max)\n",
      "ax2.set_xticklabels([x_min, x_max], [\"$x_{min}$\", \"$x_{max}$\"], size = 15)\n",
      "ax2.set_yticks(eigvals)\n",
      "ax2.set_yticklabels([\"$n = %d$\" % i for i in range(0,len(eigvals))])\n",
      "\n",
      "pl.savefig(\"konwent_num_psi.png\")\n",
      "pl.show()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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       "text": [
        "<matplotlib.figure.Figure at 0xcdd396c>"
       ]
      }
     ],
     "prompt_number": 92
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# WYKRES GESTOSCI PRAWDOPODOBIENSTWA: \n",
      "\n",
      "x = np.linspace(x_min, x_max, N)\n",
      "eigvals, eigvecs = EigenvalEigenvecProblem5(N, x_min, x_max, N_eigvals, potential, *args_potential)\n",
      "\n",
      "fig, ax1 = pl.subplots(figsize = (8, 5))\n",
      "ax2 = ax1.twinx()\n",
      "\n",
      "for idx in range(N_eigvals)[0:6]:\n",
      "    \n",
      "    psi = 9.0 * eigvecs[:,idx]\n",
      "    ax2.plot(x, psi ** 2 + eigvals[idx], label = \"$P_{%d}(x)$\" % idx)\n",
      "    \n",
      "ax1.set_ylabel(\"$P_n(x)$\", {\"fontsize\": \"xx-large\", \"rotation\": \"horizontal\"})\n",
      "ax1.set_yticks([])\n",
      "ax1.set_xticks([])\n",
      "ax1.set_xlabel(\"$x$\", {\"fontsize\": \"xx-large\"})\n",
      "ax2.set_xlim(x_min, x_max)\n",
      "#pl.ylim(-shift, shift * N_eigvals)\n",
      "ax2.set_xticklabels([x_min, x_max], [\"$x_{min}$\", \"$x_{max}$\"], size = 15)\n",
      "\n",
      "ax2.set_yticks(eigvals)\n",
      "ax2.set_yticklabels([\"$n = %d$\" % i for i in range(0,len(eigvals))])\n",
      "\n",
      "plt.savefig(\"konwent_num_P.png\")\n",
      "pl.show()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": []
    }
   ],
   "metadata": {}
  }
 ]
}