{
"metadata": {
"name": "",
"signature": "sha256:aaca15c34548da2b25e449588d079a4ac16a3b14aefe7c47d4142b1cf3a756cd"
},
"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": {}
}
]
}