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diff --git a/Modern_Physics/Chapter6.ipynb b/Modern_Physics/Chapter6.ipynb new file mode 100755 index 00000000..76cd1700 --- /dev/null +++ b/Modern_Physics/Chapter6.ipynb @@ -0,0 +1,268 @@ +{ + "metadata": { + "name": "", + "signature": "sha256:846e8e3b3770f7cb30a2e91a53718bf5de841338951843c54481c2acfda5e63d" + }, + "nbformat": 3, + "nbformat_minor": 0, + "worksheets": [ + { + "cells": [ + { + "cell_type": "heading", + "level": 1, + "metadata": {}, + "source": [ + "Chapter 6: Quantum Mechanics in One Dimension" + ] + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 6.4, page no. 197" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + " \n", + "\n", + "import math\n", + "\n", + "#Variable declaration\n", + "\n", + "me = 9.11 * 10 ** -31 #mass of electron (kg)\n", + "h = 1.055 * 10**-34 #h/2*pi (J.s)\n", + "dx0 = 1.0 * 10**-10 #initial location of electron(m)\n", + "m = 1.0 * 10**-3 #mass of marble (kg)\n", + "dx0m = 10**-4 #initial location of marble (m)\n", + "\n", + "#Calculation\n", + "\n", + "te = math.sqrt(99)* (2* me / h) * dx0**2\n", + "tm = math.sqrt(99)* (2* m / h) * dx0m**2\n", + "\n", + "#result\n", + "\n", + "print \"The time elapsed for electron is\",round(te/10**-15,1),\"X 10^-15 s and that of marble is \",round(tm/10**24,1),\"X 10^24 s.\"" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The time elapsed for electron is 1.7 X 10^-15 s and that of marble is 1.9 X 10^24 s.\n" + ] + } + ], + "prompt_number": 1 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 6.5, page no. 202" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "import math\n", + "\n", + "#Variable declaration\n", + "\n", + "m = 1.0 * 10 **-6 #mass (kg)\n", + "h = 6.626 * 10 **-34 #Planck's constant(J.s)\n", + "n = 1.0\n", + "L = 1.0 * 10**-2 #separation(m)\n", + "\n", + "#Calculation\n", + "\n", + "E1 = n**2 * h**2 /(8*m*L**2)\n", + "v1 = math.sqrt(2*E1/m)\n", + "\n", + "#result\n", + "\n", + "print \"(a) The minimum speed of the particle is\",round(v1/10**-26,2),\"X 10^-26 m/s.\"\n", + "\n", + "\n", + "#Variable declaration\n", + "\n", + "v = 3.00 * 10**-2 #speed of the particle (m/s)\n", + "\n", + "#Calculation\n", + "\n", + "E = m* v**2 /2\n", + "n = math.sqrt(8*m*L**2*E)/h\n", + "\n", + "#results\n", + "\n", + "print \"(b) We get n = \",round(n/10**23,2),\"X 10^23.\"" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "(a) The minimum speed of the particle is 3.31 X 10^-26 m/s.\n", + "(b) We get n = 9.06 X 10^23.\n" + ] + } + ], + "prompt_number": 3 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 6.6, page no. 203" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "\n", + "import math\n", + "\n", + "#Variable declaration\n", + "\n", + "L = 0.2 #length of the box (nm)\n", + "me = 511 * 10 ** 3 #mass of electron (eV/c^2)\n", + "hc = 197.3 #(eV.nm)\n", + "\n", + "#Calculation\n", + "\n", + "E1 = math.pi ** 2 * hc**2 /(2* me * L**2)\n", + "E2 = 2**2 * E1\n", + "dE = E2-E1\n", + "lamda = hc*2*math.pi / dE\n", + "\n", + "#result\n", + "\n", + "print \"The energy required is\",round(dE,1),\"eV and the wavelength of the photon that could cause this transition is\",round(lamda),\"nm.\"" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The energy required is 28.2 eV and the wavelength of the photon that could cause this transition is 44.0 nm.\n" + ] + } + ], + "prompt_number": 5 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 6.8, page no. 211" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "import math\n", + "\n", + "#Variable declaration\n", + "\n", + "h = 197.3 #(eV.nm/c)\n", + "m = 511 * 10**3 #mass of electron (eV/c**2)\n", + "U = 100 #(eV)\n", + "L = 0.200 #width(nm)\n", + "\n", + "#Calculation\n", + "\n", + "d = h /math.sqrt(2*m*U)\n", + "E = math.pi**2 * h**2 /(2*m*(L+2*d)**2)\n", + "new_U = U - E\n", + "d = h/math.sqrt(2*m*new_U)\n", + "E = math.pi**2 * h**2 /(2*m*(L+2*d)**2)\n", + "\n", + "#result\n", + "\n", + "print \"The ground-state energy for the electron is\",round(E,3),\"eV.\"" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The ground-state energy for the electron is 6.506 eV.\n" + ] + } + ], + "prompt_number": 7 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 6.13, page no. 217" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "import math\n", + "\n", + "#Variable declaration\n", + "\n", + "m = 0.0100 #mass of the spring (kg)\n", + "K = 0.100 #force constant of spring (N/m)\n", + "Kh = 510.5 #force constant of hydrogen (N/m)\n", + "h = 6.582 * 10**-16#Planck's constant (eV.s)\n", + "mu = 8.37 * 10**-28#mass of hydrogen molecule(kg)\n", + "\n", + "#calculation\n", + "\n", + "w = math.sqrt(K / m)\n", + "dE = h * w\n", + "wh =math.sqrt(Kh / mu)\n", + "dEh = h * wh\n", + "\n", + "#results\n", + "\n", + "print \"The quantum level spacing in the spring case is\",round(dE/10**-15,2),\"X 10^-15 eV, while in case of hydrogen molecule it is\",round(dEh,3),\"eV which is easily measurable.\"" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The quantum level spacing in the spring case is 2.08 X 10^-15 eV, while in case of hydrogen molecule it is 0.514 eV which is easily measurable.\n" + ] + } + ], + "prompt_number": 10 + } + ], + "metadata": {} + } + ] +}
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