{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Solving the Schrodinger equation numerically\n", "\n", "Author: Audun Skau Hansen ✉️ \n", "\n", "The Hylleraas Centre for Quantum Molecular Sciences and\n", "The Centre for Computing in Science Education,\n", "2022\n", "\n", "\n", "---\n", "\n", "## Finite difference schemes\n", "\n", "You may be aware that we have quite an arsenal of numerical methods which may help us solve differential equations. (If not, take a look at the section on discrete calculus.) This is also true for the Schrödinger equation, at least in the one dimensional case. \n", "\n", "Amongst these, *finite difference methods* consists of essentially two steps:\n", "\n", "1. Discretization of the variables: $x \\rightarrow x_n := n\\Delta x$\n", "2. Discrete approximation of differentials; $\\frac{d}{dx} f(x) \\approx \\hat{D}f(x) = F(...,f(x_{n-1}), f(x_{n}), f(x_{n+1}), ..., \\Delta x)$ \n", "\n", "In the following, we'll use the *center difference*\n", "\n", "$$\n", "\\frac{d^2}{dx^2} \\psi(x) \\approx \\hat{D}_{\\frac{1}{2}}^2 \\psi(x) = \n", "\\hat{D}_{\\frac{1}{2}} \n", "\\frac{\\psi(x + \\frac{1}{2}\\Delta x) - \\psi(x - \\frac{1}{2}\\Delta x)}{\\Delta x} = \\frac{\\psi(x - \\Delta x) - 2\\psi(x) + \\psi(x + \\Delta x)}{\\Delta x^2}.\n", "$$\n", "\n", "(make sure to derive it for yourself if it seems unfamiliar.)\n", "\n", "Numerical methods may have limited precision, but typically broad applicability. Let's apply this to the one dimensional time-independent Schrödinger equation.\n", "\n", "## Solving the Schrödinger equation numerically\n", "\n", "Our starting point is the time-independent Schrödinger equation:\n", "\n", "$$\n", "\\Big{(}-\\frac{\\hbar^2}{2m} \\frac{d^2}{dx^2} + V(x) \\Big{)} \\psi(x) = E \\psi(x).\n", "$$\n", "\n", "Using the center difference, we obtain:\n", "\n", "$$\n", "-\\frac{\\hbar^2}{2m}\\Big{(} \\frac{\\psi(x - \\Delta x) - 2\\psi(x) + \\psi(x + \\Delta x)}{\\Delta x^2}\\Big{)} + V(x)\\psi(x) = E \\psi(x).\n", "$$\n", "\n", "Next, we define $\\alpha = \\frac{\\hbar^2}{2m \\Delta x^2}$, $V_i = V(x_i)$ and $\\psi_i = \\psi(x_i)$, and rearrange our expression into\n", "\n", "$$\n", "-\\alpha \\psi_{i-1} +(2\\alpha + V_i)\\psi_i -\\alpha \\psi_{i+1} = E \\psi_i.\n", "$$\n", "\n", "We shall assume that $V_0 = V_{N} = s$, where $s$ is some large number. This is done in order to force $\\psi$ to be zero in the end points.\n", "\n", "## An Eigenvalue problem\n", "\n", "If you now stare at the expression above long enough, you may realize that it can be cast as a matrix-vector relation:\n", "\n", "$$\n", " \\begin{bmatrix}\n", " \\ddots & \\ddots & \\ddots & \\ddots & \\ddots \\\\\n", " \\ddots & -\\alpha & (2\\alpha - V_i) & -\\alpha & \\ddots \\\\\n", " \\ddots & \\ddots & \\ddots & \\ddots & \\ddots \\\\\n", " \\end{bmatrix}\n", " \\begin{bmatrix} \\vdots \\\\ \\psi_{i-1} \\\\ \\psi_i \\\\ \\psi_{i+1} \\\\ \\vdots \\end{bmatrix}\n", "=\n", "E\n", " \\begin{bmatrix} \\vdots \\\\ \\psi_{i-1} \\\\ \\psi_i \\\\ \\psi_{i+1} \\\\ \\vdots \\end{bmatrix}.\n", "$$\n", "\n", "This is actually a what we call an eigenvalue problem, typically solved using a suitable diagonalization-routine. In our case, we shall use the ```numpy.linalg.eigh```-module, which is tailored for Hermitian matrices as the tri-diagonal one above. Now, let's get coding:" ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "scrolled": false }, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "/var/folders/s2/s91psjjx77g3znkybg2ng_b40000gn/T/ipykernel_4000/3420600210.py:6: DeprecationWarning: `np.float` is a deprecated alias for the builtin `float`. To silence this warning, use `float` by itself. Doing this will not modify any behavior and is safe. If you specifically wanted the numpy scalar type, use `np.float64` here.\n", "Deprecated in NumPy 1.20; for more details and guidance: https://numpy.org/devdocs/release/1.20.0-notes.html#deprecations\n", " colorx = np.zeros((3,5), dtype = np.float)\n" ] }, { "data": { "image/png": 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\n", 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\n", 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\n", 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\n", 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\n", 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\n", 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rfmLxAVUXAsejxHZUtzvxKC12vb54QdXvNI0ocK1umLZ4kFaT70+wf2pYosRQn5MtQ0V1wywC7gJcGvz00PlVQ60jJEWx2/n2R6rLHylQJ+h3dMOsScf7CArdMAtR2U0zgKdOPWbaKodDm8/ofpfx6J46vrhl/oyyO1Ga82vdMBckcbzMiy6Ap7bxANTK/mHAiZ7axlN7/5Fl4QXdMIt0w2xAtaX8BbAAlWlxBTAzFPB+ZeWy6rf9Qd9SoBG1yPQuKfBuB6F9clXRlhkTi2+zHt+uG6Yd8dKPoBrOjzZzYivwESvVLN1cBxwMvLH8iCk+lN0Jx9BHSHRChfvNqeOLH0bdvQUkzJBWbkCtKawvKnScXVFSoKPCealm46Hzxr1bVOj4I8o5vFc3zJJhXpOdebpWJdpq1EkxmJEx1HSJwbDV07WuqhejRgtNtza/BnwXuCcU8PYA+IO+cuAM4EDUwlG606M2H7tw4s7fPfHuM7EYx6JiyXXpejMrlruc5H/ce1He7q+TNioOumEei7oYRoDPTah0Hwq0p+v9LLYcWVP1z/Vb24+IxTgeuIT4E6+FUaIb5pmoDoQ9QO0Zx88cB1QD4TS8XUTTtMjJR0797R+fea8GOAT4mW6Y5w+R0ZC14QU/yiM4C+U9eQb8m0uGY7pWzLYOFUb4KUpwW1ALfQtDAe/d/QR3LmqY5lxUyzg78lHbHZpWsXhB1SqUoKzUDXN5Gt9vLqrx/K4kj7MF5e2mZaVfN0wn6gKkATeuXFb9OrCQ1N56Dkanu8DprJ5c8j3r8fd1w7Qtfp0P6IY5F7jdevi1lcuqnwM+jup1nC42lhS5Dpk+sfgC1Hl2HnDhKI6T8Tzdw4GV4eamh+Lt4KlttD29qBfdMFcA30fZCcqzvRp4IBTwfpBuZMU4Pwas4MNlsHbQtmBmec0Lb7RdjyqfvlU3zEWhgDdesUIy6CQvuL10osJK96foeP25BBWuagWuR/X2AHvCVbuWHjyxvXXTuvtQDkUTcLoN7zvmsS6mv0aVl98P3IIK8U1HOTrpIgr0fGzRpImrH193iWXDj3XDfCwU8A5W3p6d2QvAW6iV/tGQtj9KN8zFumH+FfgLSnA3oFLaFoUC3vsHCG4F6qq3AhW7TVe8cCh2AdM+ecy0e4HXUZkF/5PqN/EHfTNQnc9S5VFsBhZbTcRThlUEcb318H9WLqvuQi1mbk7l+wxBGzD34DkV16Li3qfZtciZB3wZOA6VlvmFlcuqNdS5l45Y7kA2Aked/bGZDwP3AmXAr0YYt894eOEK4CpPbePcIfaxLbygG+Yk3TADwD9QccudgAkcEAp4f9kbRujF6qr1ZVTq1DukZ7EsUfaUlxQcjVq8A/hmGm5rjyV+qe9oiKK+3yOG23GE3IAaqfMo8AdgPuoESYfnH4/uQ+aOm4mK+QPcbBVoCKPEyhroDdvUhwLeNlS4awYpzgyKQxToKXA5jgUaUHe0y4D6QfbN2t4LN6A+sLWe2sZ3GDzn00jSpmGxToYvoqpOxqGC8z8BvhsKeD/k1VnhhOOAU1AffCa824FsAw5cuaz60dWPr2sGalENhT6dioP7g74q1AyxVLdo3AQc7w/6nk5FT1rdMJcAX0DF0y8NBbwxf9D3Uew5KfuzGTjm0Hnjbv7XWzsuRi0WX4wsqo0Ky5v8FSob6K5QwPugNUx0BSPPFU+GjcDRK5dVP7368XUNQDPwA90wHw0FvG/32y9rwwv/RnUTuxvVZeyVQf7FIyV/lFU++E+UyI5DhRQOCQW8V8QR3HLgv1GCu57sEFxQV9AuYAnqDqIdOFs3zGNSdPwjSE8vjG7UrKqFyR7I6t72Q+vhj0IB7xvWuPQ52HtigtWq9MDZFfOAr1nbvqMbZpXNdowVvoQKEW0ELrO2zUNlLOyw0Y6o9e/YUMD7O+AeVP/o26zf33DkxLieRXGeSkp0dcOchvIEV1qb3kHFQR+IlwbiD/rmoNKxCklv0H60bEJdhZ9c/fi6HwNXATfohrksmS5J1rjx46zjp4OtwIn+oO/F+rqGZEI0p6IWNLfRdxt6FOpilAm2AfqxCyf++Jl/b30COBFVOZjyePtosVIhT0MJ2BbgoVDAm/H2m/3RDXM6fWGaL4YC3u39vFw7YrkD2Qgc4w/6nkaFF0+2bPkMyvOFbPJ0PbWN5w7MSPDUNlZ7ahtdA7ZN99Q2XkWKrwxWCtjFqEyElahRON8CDgoFvH8YTJz8QZ/TH/SdgLo97EIF8bORCOrLPgz4AeoHeSLqB5EMC1HeaLrG7rSjxhLNH+0BrFVtr/Xw+lDAu9Mf9JWhPH+7FtAGsheYUD25ZA5KaGPAl3TDnJMhe/ZDN8wzUOGi36OydH4FvK0b5pVZVtTxQ1SZ74OhgPcP1rZ5jK4MPRVEUN7ucdYFyrS2/1g3zArr/7MqT/cu+p1cVh/dMDDQo52FqiaKx4ivJLphHgg8icoPrkSFNg4KBbzXhQLeQbv+Wyvr56HyANcz+iosu9gMnLByWXU7fSJ0w2hPIn/Q50ItFqQ7DW4ncEISrz8PdXF4B/iZtW0R6jeZ0QVO4PhQwPsS8FvUxWtVBu0BQDfMy4D7gMnAy6jUq8dQC47fA/zZILy6YS5D3V12oLr19RbonExmBLeXjcBSq2PeL4DngGmo3jFDkRHRHUwshxLQpLMXdMN064a5CvgXKi60CTXp4FOhgPedeK/zB3017J+dkLUDFvvRiRoKeSAqP/R9VLezs0d5vAWoC1S6K7l2ALNHUxqsG2Yxfa33rgkFvJ3+oK8AJeKZ8nJ72U5fEci1qN/Q53TDPChTBumG+WngR6hz6Erg0FDAe1ko4F2BCjV0oFIkb8qUjfBB6ONW6+F3QwFvb7XZAlSflh2ZsMsigvouP2alkH4R5f1eavXQzp7wwiiIJ7oVcbbvh26YH0N1/7oW5WUEgANDAW/zELHbIn/QdxqqY9hu1FUtl9gGrFi5rLqTvivv9dYteMJYcbNUlPwmSjuqyflIaUCdhC+ieuaCGqldxv4joDJBDKsIJBTwvoX6/TnoyyO2FUvs77AeXh4KeL39z4NQwPsQKjbeDVymG2YmizouA2pQfU5+APs1W8pk4/5eNgJH+oO+yaGA90WUk+Ogr2PiYGQ8TzcZZnpqG+MmnOuGWa4b5m2ocEINqmjghFDAe7GV3zcoVsvBRtQCTJj0e3jpYA8qRroAK06HKpj4zAiP40HdMqWqAm04tgILrYyDhLAauH/Denh1KOCNWifmCrLjxATlbR9hpd1dh1pHOFM3zHh9RdKCddG9HbXafjfw48H2CwW8IZQHDKqJku1N2a33/Kb1sLFfdeVCYBLZEeaLotZ4etdMvoVajDyuorBgTpzXZEx0B3vjeMbE276XOD1krTjQy6ik5W7UredhoYD3b/EM8gd9bn/Q93FU+aiGWmDIqg5nI2QHytuN0BfbvTrROF2/1WE781tjKM/0+BG85kuok/BZ1CRpUBeYKrInnS+Kuh09NhTwvo9KT4S+DAu7uATlTGwAGobJaPkRKn1yPH2/Hzu5DnWn8lAo4P0LfJBF80kyHzLqz0bgYH/QNycU8O7EulBUuguX2BVf0GKxoXXKU9sYRQlC//joxEG2uVCxxMNRsdiBvA9MAcaHm5t2wgdejxd1IoLKvz0/FPC+PJRNVqOas1B5uhvI7MJLKvEAd65+fF0YeBN1C35WKOAdtteB9ZlchP2pcRpqltpP6usahgzr6IZZjrobmQB8PBTw/sVa+OudypstogvgRBUC3bz68XUx1OdaAXw0FPD+X7rfXDfMCag7ngrg7FDAe18Cr5mPypUvRF0wbJn9Zk2CeBF1Hi4MBbyvA/iDPh019GCdHXaMgHGou5efrX58HSjdOaSto5OdnR/qeXVhuLnp9oEbkyGRPN3hVvcGEq+UtQvlWR8APG/Fbm9HlQX2erffDwW8cTt9+YO+StQq6GLUrW22fZnJshX4xMpl1T9Z/fi6G1Ee1jW6YQ6aGtdLv9Vhu6u4QHm77aiT6+5h9m1ECe7TwF+tbQtRF/F30mTfaImgfpcnhALe+3XDvAXlFV3LCFL6/EFfIcqzdwKb6usaEi1tvhwluH9lQIMhKxwzHfXZb6+va2gHCAW8b+qG+QNUk6ebdcM8NtF8b+uYU1CasLX3mMNhFRjcjLr43tpPcCejfhOJzuOzkx2oApwjQgHvc7phXg78tdJdyJ6uHiLDOKLJMqynO1I8tY11qFSbgbwNzHVq2umzKkpPwkonQXnFnw8FvIN5x8AHP9wl9P3Y3ye3QwlDMQdoXv34utdRXuEU4NRQwPuneC/wB30LUWPV09GbNFE8wM/r6xoGtcHKh3wHFUZYHgp4/9cf9BWjFl/aUZ5HtqGhnIifrX58XTvq861A5XsONYS190J4BGphswT1e40AfwOeqq9riJtZY3m576Bu1z/wWK0Q0mGo6spS+qqtngSerq9r6LLuHsOoC9knQgHvnz/0BvvbqaFKnk/vZ2cMeMI65pAXCWvh7gHU4u18qxDCgWqjOAUVM81GClGf0S31dQ1tx17wtXfdLufM3V3dbNu33598Qbi56Y5UvrGdC2kawIRi920owY2gvNuj4gmuP+hz+YO+Q1FX/d5xM+8xdgUXVMzptJXLqp30lch+M17JohU3O430VZ8lynbgTOsCORiXogT3KfpGuuuoEz0bBRfU72w3cPrKZdU76YvtXjvUi6zP4Czr317UesN6lACtAM63CkHicTlKcB/tJ7gF1vFqrWOus465GSXsn/cHfRWhgHcPcKN1nO8MVepqhXbOQJXJ9x7zXdRv8CTgIqsr36BYKWK9v9FV/crwj6avYi5b6UJp0Fn+oM+5raPzH7FYjLICF4WO/WQxJ7IXPnSLqwEVhQUTAJyaNh3Vw+GoUMB7bSjg/VDJpz/oK7DE9jLUj6wD9YPIVHmonXSgbvFWALehxGwpqlJtME5CCVemszZ2okIHH1pU0w2zEtVfAuBaq6nNLGvflE75TQPbUbH1o1GLVbuBk3XDXDrYzv6gzw2ci/JI32H/FLgea9tM4MLBBE03zIn0xbhXWccsROWpL45zzFZU1spFVnGQDyXGS1DpZIPZWYDKjlmC8oz7X/h6jzkeuNgqKBiMBlTGzetYBS7+oG8maup0qhstpYNNqIvDcV2R6O5dXd1omsb4Ynda3zQdortfg2C308H0shIKnY4KAKdDuwk4MhTw/nPgC/1B3zirw9TXUWLb++VnWlDs5j1UTwYP6kSHvnScD/AHfQeQXcK1HljhD/oGlgdfhlq8eCIU8IYssTkXdUsaJftZD3xq5bLqMtQ0EhjE27XuOj6LOpHXEd9Leg+16HyhtU7Rn14v98+hgPdZS8TrUJNaWoc45kbUxfcLK5dVF9Dn7a4a6O1agnsOKqzwzhDH3ISaFHPhQOG1QiC9n8FXQwFvtz/omwB8jg8vsmcz64FPVE8oGbezo4tINEaRy0mJ64MU+ZR7uumI6R6AuvJR5S6kwl2Apmm8v6c92hWJvvx2c9Nh/ff3B32lqDjmElS5cQx1lbazl2o24gYmr9u0N/jMK9vWoGKJx4cC3qfhgwblBuoHnk0XpRKUwPrr6xre1w1zHOrErkSVOz+PEqbp5FYRSwXgfuPd3ff+8z9tz6OE8ZhQwPscgD/oK0Hdps8g8YvgFNRt/R31dQ3bLS83bB176cpl1S0o52MeiXuOk4Cu9VvaV//fy1uft97j9FDA+6BlZ7F1zAUkvhA9CSWid9TXNWwCsBYWL0WVIp+8cln1eOACVKzU7kksyeJ+ed2Oi599Y+vCrs4YE4rddEeibNjTDnBeuLnprlS+2ZCi++07//DESA+4fdfu4kee/vtRPdEY5YUFlLic7OjsojMS5YTDD2mZO33SLgeRAqcWKXRp3aVOLeLWgGhMi8TQejI8qT2r0Ig6NS3mWtu6o+A/72ycXlFRvn3xooNedmk9xcWO9smxGJEYjqxLl9OIujQt5twXLd782pvvTd7w/qbZ5WWlO5YcdtCrxY69kx1EC6I4c+6iav1djlfDbYVvrdtkfR8Hv+ykx13s3DtJi8WcUZwjCoE5iBSgoe2Llm5+5T/vTn1/4+bqivKy7UsOrXmj2Nk+SYtFR3xMjWiBpqG9uX6X47W3NlSXFBftWbL40BdcWqSwyNE+yUHUNYpjujQNR0e0aOv23d3RF1769xJAO3zRQf+YWOmOFTk6JhGLxaI47ZgzmHLeePe9aV1dneXvbNlDrFPDoWls29fJgfM9aw/yVI94veTaz59xYrzn0tIZf3yRm9IiF1WVBcRiMWY4iikqcEUWzSoq19g1TiPm1Ig5YhCN4ojEIKZpMadGbERlr/mARsz5kZnluKJ7Y92R6HhX99Z5pUUuIKZFNYemEcnK6QYaMWcRe2ZUFO6bWjyjjFnTJ+8tc+6aqRFzRXF0O4ikN3CWJhxEXQdWV2gFtMd6ItHxzq7N80qLC2IaMUdUc/SM5u/SiDmLYrtmjXPvm1o6o4zq6VPaS527Z2jEnFFtdJ+VRsy5YEap5ohURjq7esro2HRAaZm7RyPmHO3nrxFzljj2Ttu+r61q/oxSraK8bOf0cbHxTm2vO4YWi2laJFe/16ICh6OrC2pmVNLZGaHA4WDcDqVfqSYd4YX5Tk37z8RSN5XlBURjMXqiMWKx2Ht1x8/5JBI2GBVrXtl6bVdP9ByXQ/vbcYdM+iI5kMERenHzpZFo7JLSIueLSw+e+A1ULDMXYrjDoT336rarOrojn3U6tOeOP2TShST5fYRe3HR5NMpFJUXOf1if1cZkjwnw99e2XdLRFbkUtNeOP2RircOhJXVn9MIb24/aurPrjhK3s2Ohp/ILVeWFb5OZ/PCUcteT4Rs7uiOfAnA5HEwqc/P+jn1s29v13+HmpuHyz0dEOkR3HqqaaiDhcHPTULPVhCGwGkOHUU2ADg4FvK9l2KQhGRCfHDavNdcY8PclVf1lDeYMo3Jvjw4FvH9PjZWgG2apdexJwCmhgPfRJI7lQM0jPBz4ZijgzUgToHTgqW38LWrBciApF107u4wJSRAKeN9DVfD1tvfLdq6gbxV+TAkuQCjg3Upf3u6qJA93BUpwH0ml4AKEAt699OXSXpvgiJp4fA4luOtRVWj5QE7k6cZDVsiS5/uohO5zdcPM2rsG3TAno/oawzCFBDnOTfTl7R43mgNYn1XvROiRltwnig/VwW0pqsH9iLE85t6GP1eFAt5syphJBWOyn66IbpJYTaF/i6rj/3qGzRmKr6E8t4dS7bllE1YFVm8e9WgF82rUZ/Vwuj4rq0qtt8H5t0fp7V6BSvN7geF7bOQiOd1PV8IL6eUG1Gd8gW6YMzJtzECsvqq9XePGspfby49QC0knWZOqE0Y3TA9qgkEMNZQ0ndyKyp89DvivkbzQWk/o7YF8uTV5IV/ICdGNh3i6KcBaQLsPlYR+xTC7Z4KvA8XAHwarOhxrhALeHfTFN28e4bSP76EWRu8OBbwtqbatP6GAdxd9secbdcMsGMHLr0cVvdw/VI/rHEfCC8KQ9I63rrdiglmB5RF90Xq4KoOm2M1NqIqxxagqwWHRDXMFfdOtP1TinSZ+DryBqka7PJEX6Ia5GDUGq4c+bzefyAlPV8ILacaa7/QwyvvIptiuCRQB9w7VqnOsYWUI9IrYDbphzhxqf2swp896+J2hhq2mEqtXdW8znW/rhvmRofbXDdMN3IlymH4aCnj/k2YTM0lOx3TjIZ5uaukdffQly8PMKLphzkKNW4qRX15uL/cCj6D6TvxWN8xBKwWtRazbUH1GXsHmCb5Wnu7tqN4ev9YNs2iI3a9HNZl/E/u88Uwh4QVhaKx46X0ozzIb8na/g4oz3xMKeP+daWPsxprQcAGqwf5HgZ/EmW/3FeA8VJOiuqEmpaSRK1DNbo4C7hjMTt0w64GvoioIz7O8+XwkJzxdCS/Yx7Woz/ti3TDjjUlKO7phHgJ8HjXe5ppM2ZFpQgHvZlRVUxcqtn27bpjjAXTDLNIN83v0pZgZw80CTKOdbaiet7tRLR7v72dngW6YV2H1xwW+ZNestQyT055uPMTTTTGWR7ka5WFmUuxuQH2/t4UC3rcyaEfGCQW8T6IEbR/Kow3rhvkUaqHtSlRxy8WhgHewkVa2YQn+Gah0t9OB9ZadraiFWg1VBHFbxoy0l5yO6Yqnay/fRt0CXqAb5gF2v7mVm/pJ1CTfMVOLnwyhgPevqHzYx7D6IKPmcb2I6n8QyKB5HxAKeB9HlfWGUGl+x6MmULwNrAgFvDdk0LxsIadFVzzdNGBNX70d1abzh8PsnlKsRaHeCQU3WrfXAirDJBTwrgBqgBNQ4nZEKOB9LLOW7U8o4A2HAt5lKLH9JHAgcEC22WkDtumTnb1YRXTTxzWoaQCn6Ya5wvK07KAOtRizib5YpdAP66L4eqbtGI5QwLsRlX2Rr0h4QUgc64TpLZj4Ubx0pVRijVTvTXe62qrvF4SxRk6IbjzE000vt6D6ph4MXGzD+60CpgLPosIbgpDL5HT2gsR0M0Ao4O1A5VUCXGdNa00LVorYpagFvC/lWQMUIb/ICU9XwguZ437USvR40lTpZC2e3YpqL/mzfGhqI+QFOR3TjYd4umnGqoq6BOgAPq8b5ilpeBsDVXG1hbFfGirkDxJeEEZHKOB9g74+tr+0ZnmlBN0w59HXxvArVmWTIIxlcsLTlfBC5rkZeBrV6f+XSc7FAj7oOHU3asrBPaGAN5jsMQUhi8hpTzce4unaRCjg7QE+S1+JZyraP/4IOBpVztqQguMJQjaR0zFdCS9kAaGAtxXVhAZUj9cRjWjpj26YX0I1cOkCzrZmgwlCPpDToivYTCjgfQA1+FADVuuGuXykx9ANsw74qfWwPhTwPp9CEwUhW5DwgpAybgD8qL67D+qGeUaiL9QN8xLgN6jv7spQwHtHOgwUhCwmpz1dEd0MYKWRNQABlPDerxvm9dbC2KDohlmuG2YA1VPVgZpS8X077BWEDGFbTDcdNfoSXsgyQgFv1JoE8BbK870aOEc3zJuA34cC3q0AViP0z6AmC0wDOlEVZ7/MjOWCYBvSZUxILZbH+33dMJ9FebAHWv/9mW6YW1EVZlX9XvICcH4+jt4RhH7ktKfr8NQ2lqbh/bKFfeHmpqzvQRAKeJ/UDfMw4NPAF4BjUA22QY1vCaFCEQ9bQi0I+UBOe7rxTtRy1HSBsUqbp7bx98Cl4eamjkwbMxShgLcL+C1qaq0D1S2sC2gLBbyRjBonCJkhp2O6+UoVqi+BA7gow7YkjNUh7L1M2yEIWUpOZy/kC3We2saiTBsxkKqapXOqapbGqmqWnt9v2z+qapbe0e/xqqqapfn+/Qn5SU7n6e5GjW/JV0qAWZk2QhCElJD9nm64uSkG3Jnq4+YYMzNtgCAIIyLnY7pXAu3AOcDsNL1HNuBGpVoNJBtFt8f6b9yiCFTxRM8QzwvCWCWnsxewUqe+bf0bs3hqG29Bja0ZyAy7bUmA3t63Q4U+qvvtJwhCLoQX8owNcbZnnafbtnbNXlRF2hGDPV9Vs1QDFgP/stMuQcgSctvTzSPWx9medaJr8Xvg61U1Sxe2rV0zsNLsdOAj9JutVlWztBQ1D20pKuxwa9vaNT67jBWyB09t4wSgJtN2pJFxcbbnTEw3X8g10b0ROA9YXVWz9IP+ulU1S49GdSJ7Ebij3/43AW+0rV1zvrXf5P4H89Q2VgBHAZVptTq7aAeeCTc37cy0IXbgqW0sRC2Mn0N+lvKL6GYZOSW6bWvXbK+qWXoK8BDwBmqE+iGoZuf/Aj7VtnZNN0BVzdJy4Az6xYDb1q7Z3Pv/ntrGk4B7gLSNes9iIp7axgvCzU13ZdoQG7gaWJlpI8YSEtNNjniVXFMsDyHraFu7pgU4GFU1txn4N1ALHNW2dk3/v2cuauLvLVU1S/9ZVbP0gaqapXMArB4ad5GfggsqY+VOT21jNi6YpppPZdqADJPyfioiuklg9VjYEufp6XbaMhLa1q7Z3bZ2ze3A+8DLbWvX/K5t7ZquAbu5gIXAA21r1ywGHqAv//p0VOvHfEYDRjyJIweZkmkDMkgMaEn1QUV0kyenQgwjYD2ws23tmketx6vpy3w4NzMmZR3jM22ADWTlHZtN/Dzc3JTyeYAS002e9cDhg2x/ylPbaLctI2LcoiMAjvDUNn5+sOd2v/U6sz51QcxVUkrp7Hl0bNmIp7ZRejP0MVShyVghnuj+nbFbSLMN+DNwWzoOLqKbPPFydXOekhnVtK9vJRaNojmdlMwcsrhwD/AXm0yzm4MYPF0qH7zAeH/jsnBz015bLRkjiOgmT7zwQs7jLCqmfH7CqZmrw81NRjrtyRSe2sZrgOsGeSqfRXfgGoCQIBLTTZ5XMm1AlnB3pg1II/EEZkyLrqe20cngvUVg7IYW0o6IbvL8CWkC/gzwt0wbkUbiie5Yj+nG9XKtboLCKBDRTZJwc1Mn8FFUPHNfhs2xm93A74Czc2E+XBLkpadL/L+v01YrxhgS000B4eamt4GPe2ob865MMk88nngik6+iK/HcJBDRTSF5IkD5iIQX9kdENwkkvCAIwyPhhf0R0U0CEV1BGB4R3f0R0U0CEV1BGJ58jenGC5/IQloSiOgKwvBITHd/xNNNAhFdQRgeCS/sj4huEojoCsLwiOjuj4huEojoCsLwxIthSnhBGDEiuoIwPOLp7o8spCWBiK4gDE++im48T1483SQQ0RWE4cnXlDEJL6QBEV1BGB5JGdsfEd0kENEVhOHJ1/CCiG4aENEVhOER0d0fWUhLAhFdQRiefE0Zk4W0NCCiKwjDE280jdMaaTNWkfBCGhDRFYRhsPokxxOaAjttsRkR3TQgoisIiZGPcV0R3TQgoisIiZGPcV0R3TQgoisIiSGebh+SvZAEIrqCkBj5KLqSvZAGRHQFITHyUXQlvJAGRHQFITEkptuHiG4SiOgKQmKIp9uHiG4SiOgKQmKI6PYhC2lJIKIrCIkh4YU+xNNNAhFdQUiMfPR0JXshDYjoCkJi5KPoiqebBkR0BSExRHT7ENFNAhFdQUgMien2IQtpSSCiKwiJIZ5uH+LpJoGIriAkhohuHyK6SSCiKwiJkY/DKSV7IQ2I6ApCYuTjGHbxdNOAiK4gJIaEF/oQ0U0CEV1BSAwR3T4keyEJRHQFITHyMaYrnm4aENEVhMTIq5iup7ZRI/7f1m2nLWMNEV1BSIx8Cy/Em3LcE25uitpqyRhDRFcQEiPfwgsSWkgTIrqCkBh5FV5AFtHShoiuICRGvoUXxNNNEyK6gpAYIroKEd0kEdEVhMSQmK5CRDdJRHQFITHyLaYrfRfShIiuICSGhBcUspCWJCK6gpAYEl5QiKebJCK6gpAY4ukqRHSTRERXEBIj32K6IrppQkRXEBIj3zxdWUhLEyK6gpAYEtNVyEJakrgybYAg5AjxRHe2p7YxbKsl9lAaZ7t4ukkioisIiRHPw3MAc2y0I9OI6CaJhBcEITFEbBTyOSSJiK4gJMZuYFemjcgCNmTagFxHRFcQEiDc3NQDPJBpOzJMFPhDpo3IdUR0BSFxLgF+R37eYm8Azg03N72QaUNyHS0Wi2XaBkHIKTy1jSXAlEzbYSPdwIZwc5OIRQoQ0RUEQbARCS8IgiDYiIiuIAiCjYjoCoIg2IiIriAIgo2I6AqCINiIiK4gCIKNiOgKgiDYiIiuIAiCjYjoCoIg2IiIriAIgo2I6AqCINiIiK4gCIKNiOgKgiDYyP8DE3Yb+A8lKQsAAAAASUVORK5CYII=\n", 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\n", 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\n", 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "from scipy.interpolate import interp1d #I will use this for both the potential and the colors\n", "import numpy as np\n", "import matplotlib.pyplot as plt\n", "\n", "# some nice colors, feel free to experiment \n", "colorx = np.zeros((3,5), dtype = np.float)\n", "colorx[:,0] = np.array([0.44,0.7,.76])\n", "colorx[:,1] = np.array([0.1,0.1,.2])\n", "colorx[:,2] = np.array([0.97,0.9,.63])\n", "colorx[:,3] = np.array([0.37,0.02,.13])\n", "colorx[:,4] = np.array([0.41,0.87,.62])\n", "colorx = colorx**1.1\n", "palette = interp1d(np.linspace(0,1,5), colorx)\n", "c1,c2,c3, c4 = palette(np.random.uniform(0,1,4)).T\n", "\n", "\n", "\n", "Nx = 200 #number of grid-points\n", "x = np.linspace(-1,1,Nx) #the grid itself\n", "a = 0.5 #we are only interested in the qualitative behaviour of the equation, this is a dummy parameter\n", "dx = x[1]-x[0] # finite stepsize\n", "\n", "\n", "# construct a potential\n", "vx = -2*np.exp(-15*x**2) # \n", "nnx = 6\n", "vx = interp1d(np.linspace(-1,1,nnx), np.random.uniform(-3,-.1, nnx), 0)(x) #uncomment for random potential\n", "vx[0] = 10\n", "vx[-1] = 10\n", "\n", "\n", "# set up the hamiltonian\n", "h = np.diag(a*.5*np.ones(Nx)*4/dx**2 + 200*vx)\n", "for i in range(1,Nx-2):\n", " h[i+1,i] = -a/dx**2\n", " h[i,i+1] = -a/dx**2\n", "\n", "# diagonalize\n", "e, psi = np.linalg.eigh(h)\n", "\n", "# function to visualize the results\n", "def visualize(e,psi,i):\n", " plt.figure(figsize = (6,3))\n", " plt.plot(x,vx, color = c1**2, linewidth = 6, zorder = 10)\n", " #i = 3\n", " plt.axhline(0, color = c3**.5, zorder = -1)\n", " plt.plot(x, 5*psi[:,i], color = c3, linewidth = 2, zorder = 11)\n", " plt.fill_between(x, 0*x, 50*psi[:,i]**2, color = c2**.5, alpha = .4, zorder = 21)\n", " #plt.plot(x, psi[:,1])\n", " plt.xlim(-1.1,1.1)\n", " plt.text(-1.05,0,\" 0 \", color = c1**2, ha = \"left\", fontsize = 15, zorder = 20)\n", "\n", " ni = np.argmin(psi[:, i])\n", " plt.text(x[ni], 5*psi[ni, i]-.25,\" $\\Psi_{%i}$ \" %i, color =c3**2, ha = \"center\", fontsize = 15, zorder = 20)\n", "\n", "\n", " ni = np.argmax(psi[:, i]**2)\n", " plt.text(x[ni], 50*psi[ni, i]**2+.1,\" $\\\\rho_{%i}$ \" %i, color =c2**2, ha = \"center\", fontsize = 15, zorder = 20)\n", "\n", " plt.text(-1.1,.2, \"Energi $\\\\rightarrow$\", fontsize = 15, color = c1**2, rotation = 90)\n", "\n", " plt.ylim(vx.min()*1.1, 1.1*(50*psi[:,i]**2).max())\n", " plt.axis(\"off\")\n", " #plt.savefig(\"lincomb_%i.png\" % i,transparent = True, dpi = 300, bbox_inches = \"tight\") #uncomment to save\n", " plt.show()\n", "\n", "# visualize the results\n", "for i in range(10):\n", " visualize(e,psi,i)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "```{admonition} Discussion\n", "- Can you count the nodes? How do they relate to the energy?\n", "- How does the probability density behave as the energy increase?\n", "- Where is the probability highest for the ground state? What about the most excited state?\n", "- What happens to the wavefunction at the endpoints? \n", "```" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [] } ], "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": "3.8.9" } }, "nbformat": 4, "nbformat_minor": 2 }