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diff --git a/backup/Quantum_mechanics_by_M.C.Jain_version_backup/chapter7.ipynb b/backup/Quantum_mechanics_by_M.C.Jain_version_backup/chapter7.ipynb new file mode 100755 index 00000000..50969726 --- /dev/null +++ b/backup/Quantum_mechanics_by_M.C.Jain_version_backup/chapter7.ipynb @@ -0,0 +1,238 @@ +{
+ "metadata": {
+ "name": "",
+ "signature": "sha256:df09a01a18ea5b59bfa81431af3bf540f8785c24b7f1fddb025b95df17f9d0c1"
+ },
+ "nbformat": 3,
+ "nbformat_minor": 0,
+ "worksheets": [
+ {
+ "cells": [
+ {
+ "cell_type": "heading",
+ "level": 1,
+ "metadata": {},
+ "source": [
+ "Chapter 7 particle in a potential well"
+ ]
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 7.4 Page no 134"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "#Given\n",
+ "m=9.1*10**-31 #Kg\n",
+ "h=1.05*10**-34 #Js\n",
+ "ev=1.6*10**-19\n",
+ "n1=1\n",
+ "n2=2 \n",
+ "n3=3\n",
+ "a=10**-10 #m\n",
+ "\n",
+ "#Calculation\n",
+ "import math\n",
+ "E1=((n1**2*math.pi**2*h**2)/(8.0*m*a**2))/(1.6*10**-19) #ev\n",
+ "E2=n2**2*E1\n",
+ "E3=n3**2*E1\n",
+ "\n",
+ "#Result \n",
+ "print\"three lowest energy levels are \",round(E1,1),\"ev,\", round(E2,1),\"ev and \",round(E3,2),\"ev\"\n",
+ "print \"their eigenfunctions are 1/10**-5*cos(pie*x/2*10**-10),1/10**-5*sin(pie*x/10**-10) and 1/10**-5*cos(3*pie*x/2*10**-10)\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "three lowest energy levels are 9.3 ev, 37.4 ev and 84.08 ev\n",
+ "their eigenfunctions are 1/10**-5*cos(pie*x/2*10**-10),1/10**-5*sin(pie*x/10**-10) and 1/10**-5*cos(3*pie*x/2*10**-10)\n"
+ ]
+ }
+ ],
+ "prompt_number": 14
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 7.5 Page no 135"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "#Given\n",
+ "m=10.0*10**-3 #kgram\n",
+ "l= 10.0*10**-2 #Length in m\n",
+ "h=1.054*10**-34\n",
+ "n1=1\n",
+ "n2=2 \n",
+ "n3=3\n",
+ "\n",
+ "#Calculation\n",
+ "E1=(((3.14*h*n1)**2)/(2.0*m*(l**2)))/(1.6*10**-19)\n",
+ "E2=(((3.14*h*n2)**2)/(2.0*m*(l**2)))/(1.6*10**-19)\n",
+ "E3=(((3.14*h*n3)**2)/(2.0*m*(l**2)))/(1.6*10**-19)\n",
+ "\n",
+ "#Result\n",
+ "print\"energies are \", round(E1,46),\"ev,\",round(E2,46),\"ev,\",round(E3,45),\"ev\"\n",
+ "print\"these energies are extremely small and close together and hence can't be measured\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "energies are 3.4e-45 ev, 1.37e-44 ev, 3.1e-44 ev\n",
+ "these energies are extremely small and close together and hence can't be measured\n"
+ ]
+ }
+ ],
+ "prompt_number": 84
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 7.7 Page no 136"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "#Given\n",
+ "L=10**-9 #Width in m\n",
+ "v=9.0*10**-9\n",
+ "h=1.054*10**-34 #Js\n",
+ "c=3*10**8 #m/s\n",
+ "m=9.1*10**-31\n",
+ "v1=(9.0+1)*10**-9\n",
+ "v2=(9.0-1)*10**-9\n",
+ "\n",
+ "#Calculation\n",
+ "import math\n",
+ "n=math.sqrt((4*c*m*(L**2))/(v*math.pi*h))\n",
+ "n1=math.sqrt((4*c*m*(L**2))/(v1*math.pi*h))\n",
+ "n2=math.sqrt((4*c*m*(L**2))/(v2*math.pi*h))\n",
+ "\n",
+ "#Result\n",
+ "print\"value of n is \",round(n,0),\", When + sign is taken \",round(n2,0),\", when -ve sign is taken \",round(n1,0)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "value of n is 19.0 , When + sign is taken 20.0 , when -ve sign is taken 18.0\n"
+ ]
+ }
+ ],
+ "prompt_number": 15
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 7.8 Page no 136"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "#Given\n",
+ "L1=0.4\n",
+ "L2=0.6\n",
+ "L=1 #Say\n",
+ "\n",
+ "#Calculation\n",
+ "import math\n",
+ "dx=(L2-L1)*L\n",
+ "#for ground state\n",
+ "P1=2/L*(math.sin(math.pi*L/2.0*L))**2*dx\n",
+ "#for first excited state\n",
+ "P2=2/L*(math.sin(2*math.pi*L/2.0*L))**2*dx\n",
+ "#for second excited state\n",
+ "P3=2/L*(math.sin(3*math.pi*L/2.0*L))**2*dx\n",
+ "\n",
+ "#Result\n",
+ "print\"(a) probability for ground state \", P1\n",
+ "print\"(b) probability for first excited state \",round(P2,1)\n",
+ "print\"(c) Probability for second excited state \", P3"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "(a) probability for ground state 0.4\n",
+ "(b) probability for first excited state 0.0\n",
+ "(c) Probability for second excited state 0.4\n"
+ ]
+ }
+ ],
+ "prompt_number": 16
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 7.9 Page no 140"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "#Given\n",
+ "a=10.0**-14 #m\n",
+ "m=1.6*10**-27 #mass of a nucleon in kg\n",
+ "h=1.054*10**-34 #Js\n",
+ "\n",
+ "#Calculation\n",
+ "import math\n",
+ "Emin=((3*(math.pi**2)*(h**2))/(2.0*m*(a**2)))/(1.6*10**-19)\n",
+ "\n",
+ "#Result\n",
+ "print\"minimum energy of a nucleon is \", round(Emin*10**-6,1),\"Mev\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "minimum energy of a nucleon is 6.4 Mev\n"
+ ]
+ }
+ ],
+ "prompt_number": 17
+ }
+ ],
+ "metadata": {}
+ }
+ ]
+}
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