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{
"metadata": {
"name": "",
"signature": "sha256:8315bc6aae714998ec5db8a7cf2faf25a033ca960fbcf8e976cdfc44e47b09f3"
},
"nbformat": 3,
"nbformat_minor": 0,
"worksheets": [
{
"cells": [
{
"cell_type": "heading",
"level": 1,
"metadata": {},
"source": [
"Chapter 8: Quantum Mechanics in Three Dimensions"
]
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 8.4, page no. 270"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"\n",
"\n",
"import math\n",
"\n",
"#Variable declaration\n",
"\n",
"R = 1.0 #radius(m)\n",
"T = 1.0 #period of revolution(s)\n",
"m = 1.0 #mass of stone(kg)\n",
"h = 1.055 * 10**-34 #planks constant (kg.m^2/s)\n",
"\n",
"#Calculation\n",
"\n",
"v = 2*math.pi*R/T\n",
"L = m * v * R\n",
"l = L / h\n",
"\n",
"#Results\n",
"\n",
"print \"The orbital quantum number l is\",round(l/10**34,2),\"X 10^34.\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"The orbital quantum number l is 5.96 X 10^34.\n"
]
}
],
"prompt_number": 2
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 8.6, page no. 272"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"\n",
"\n",
"import math\n",
"\n",
"#Variable declaration\n",
"\n",
"l = 3 #orbital quantum number\n",
"\n",
"#Calculation and results\n",
"\n",
"L = math.sqrt(l*(l+1))\n",
"print \"The allowed values of Lz are\"\n",
"for i in range(-l,l+1):\n",
" print i,\"h\"\n",
"print \"The allowed values of theta are\"\n",
"for i in range(-l,l+1):\n",
" theta = round(math.acos(i/L)*180/math.pi,1)\n",
" if theta > 90:\n",
" print theta-180\n",
" else:\n",
" print theta"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"The allowed values of Lz are\n",
"-3 h\n",
"-2 h\n",
"-1 h\n",
"0 h\n",
"1 h\n",
"2 h\n",
"3 h\n",
"The allowed values of theta are\n",
"-30.0\n",
"-54.7\n",
"-73.2\n",
"90.0\n",
"73.2\n",
"54.7\n",
"30.0\n"
]
}
],
"prompt_number": 5
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 8.7, page no. 281"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"\n",
"\n",
"#Variable declaration\n",
"\n",
"n = 2\n",
"Z = 1\n",
"\n",
"#Calculation and results\n",
" \n",
"print \"The states of hydrogen atom are\"\n",
"for i in range(n):\n",
" for j in range(-i,i+1):\n",
" print \"n = \",n,\"l = \",i,\"ml = \",j\n",
"\n",
"E2 = -13.6 * Z**2/n**2\n",
"print \"All states have same energy of \",E2,\"eV.\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"The states of hydrogen atom are\n",
"n = 2 l = 0 ml = 0\n",
"n = 2 l = 1 ml = -1\n",
"n = 2 l = 1 ml = 0\n",
"n = 2 l = 1 ml = 1\n",
"All states have same energy of -3.4 eV.\n"
]
}
],
"prompt_number": 9
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 8.8, page no. 284"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"\n",
"import scipy\n",
"from scipy import integrate\n",
"import math\n",
"\n",
"#Variable declaration\n",
"\n",
"z2 = lambda z: z**2 * math.e ** -z\n",
"\n",
"#Calculation\n",
"inf = float('inf')\n",
"integ,err = scipy.integrate.quad(z2,2.0,inf)\n",
"P = integ * 0.5\n",
"\n",
"#result\n",
"\n",
"print \"The probability is\",round(P,3)\n",
"\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"The probability is 0.677\n"
]
}
],
"prompt_number": 7
}
],
"metadata": {}
}
]
}
|
