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authorkinitrupti2017-05-12 18:40:35 +0530
committerkinitrupti2017-05-12 18:40:35 +0530
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tree9806b0d68a708d2cfc4efc8ae3751423c56b7721 /Modern_Physics_By_G.Aruldas/Chapter6_2.ipynb
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-{
- "metadata": {
- "name": "",
- "signature": "sha256:8884b20a8f08880d4a94501a9f3a466664f30ca1f04c541fe7d3a232f87a24bc"
- },
- "nbformat": 3,
- "nbformat_minor": 0,
- "worksheets": [
- {
- "cells": [
- {
- "cell_type": "heading",
- "level": 1,
- "metadata": {},
- "source": [
- "6: Quantum mechanics of simple systems"
- ]
- },
- {
- "cell_type": "heading",
- "level": 2,
- "metadata": {},
- "source": [
- "Example number 6.1, Page number 90"
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "#importing modules\n",
- "import math\n",
- "from scipy.integrate import quad\n",
- "from __future__ import division\n",
- "\n",
- "#Variable declaration\n",
- "a=2*10**-10; #length of square well(m)\n",
- "\n",
- "#Calculation\n",
- "def intg(x):\n",
- " return (2/a)*(math.sin(math.pi*x/a))**2\n",
- "\n",
- "S=quad(intg,0,0.25*10**-10)[0] #probability of finding the electron\n",
- "\n",
- "#Result\n",
- "print \"probability of finding the electron is\",round(S,4)"
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "output_type": "stream",
- "stream": "stdout",
- "text": [
- "probability of finding the electron is 0.0125\n"
- ]
- }
- ],
- "prompt_number": 6
- },
- {
- "cell_type": "heading",
- "level": 2,
- "metadata": {},
- "source": [
- "Example number 6.2, Page number 96"
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "#importing modules\n",
- "import math\n",
- "from __future__ import division\n",
- "\n",
- "#Variable declaration\n",
- "h=6.626*10**-34; #planck's constant(Js)\n",
- "new0=6.43*10**13; #frequency(Hz)\n",
- "e=1.6*10**-19; #conversion factor from J to eV\n",
- "mew=1.1385*10**-26; #reduced mass(kg)\n",
- "\n",
- "#Calculation\n",
- "E0=h*new0/2; #zero point energy(J)\n",
- "E0=E0/e; #zero point energy(eV)\n",
- "k=4*math.pi**2*new0**2*mew; #force constane(N/m)\n",
- "\n",
- "#Result\n",
- "print \"zero point energy is\",round(E0,3),\"eV\"\n",
- "print \"force constane is\",round(k),\"N/m\"\n",
- "print \"answer varies due to rounding off errors\""
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "output_type": "stream",
- "stream": "stdout",
- "text": [
- "zero point energy is 0.133 eV\n",
- "force constane is 1858.0 N/m\n",
- "answer varies due to rounding off errors\n"
- ]
- }
- ],
- "prompt_number": 9
- },
- {
- "cell_type": "heading",
- "level": 2,
- "metadata": {},
- "source": [
- "Example number 6.6, Page number 104"
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "#importing modules\n",
- "import math\n",
- "from __future__ import division\n",
- "\n",
- "#Variable declaration\n",
- "m1=19.9217*10**-27; #mass of carbon atom(kg)\n",
- "m2=26.5614*10**-27; #mass of oxygen atom(kg)\n",
- "r=1.131*10**-10; #separation(m)\n",
- "hbar=1.054*10**-34;\n",
- "e=1.6*10**-19; #conversion factor from J to eV\n",
- "\n",
- "#Calculation\n",
- "mew=(m1*m2)/(m1+m2); #reduced mass(kg)\n",
- "I=mew*r**2; \n",
- "deltaE=hbar**2/I; #energy difference(J)\n",
- "deltaE=deltaE/e; #energy difference(eV)\n",
- "\n",
- "#Result\n",
- "print \"energy difference is\",round(deltaE*10**4,2),\"*10**-4 eV\""
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "output_type": "stream",
- "stream": "stdout",
- "text": [
- "energy difference is 4.77 *10**-4 eV\n"
- ]
- }
- ],
- "prompt_number": 21
- },
- {
- "cell_type": "heading",
- "level": 2,
- "metadata": {},
- "source": [
- "Example number 6.7, Page number 105"
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "#importing modules\n",
- "import math\n",
- "from __future__ import division\n",
- "\n",
- "#Variable declaration\n",
- "m1=1;\n",
- "m2=0;\n",
- "m3=-1; #m-components\n",
- "l=1;\n",
- "\n",
- "#Calculation\n",
- "L=math.sqrt(l*(l+1)); #length of vector\n",
- "theta1=math.acos(m1/L); #orientation for m=1(radian)\n",
- "theta1=theta1*180/math.pi; #orientation for m=1(degrees)\n",
- "theta2=math.acos(m2/L); #orientation for m=0(radian)\n",
- "theta2=theta2*180/math.pi; #orientation for m=0(degrees)\n",
- "theta3=math.acos(m3/L); #orientation for m=-1(radian)\n",
- "theta3=theta3*180/math.pi; #orientation for m=-1(degrees)\n",
- "\n",
- "#Result\n",
- "print \"orientation for m=1 is\",theta1,\"degrees\"\n",
- "print \"orientation for m=0 is\",theta2,\"degrees\"\n",
- "print \"orientation for m=-1 is\",theta3,\"degrees\""
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "output_type": "stream",
- "stream": "stdout",
- "text": [
- "orientation for m=1 is 45.0 degrees\n",
- "orientation for m=0 is 90.0 degrees\n",
- "orientation for m=-1 is 135.0 degrees\n"
- ]
- }
- ],
- "prompt_number": 22
- }
- ],
- "metadata": {}
- }
- ]
-} \ No newline at end of file