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-rwxr-xr-xModern_Physics/Chapter5.ipynb269
1 files changed, 32 insertions, 237 deletions
diff --git a/Modern_Physics/Chapter5.ipynb b/Modern_Physics/Chapter5.ipynb
index 175eed34..331dc531 100755
--- a/Modern_Physics/Chapter5.ipynb
+++ b/Modern_Physics/Chapter5.ipynb
@@ -1,7 +1,6 @@
{
"metadata": {
- "name": "",
- "signature": "sha256:e257dccb197e3cab0c059eb9e1d236e5359e2a825fc6be941cab77026f236087"
+ "name": "Chapter5"
},
"nbformat": 3,
"nbformat_minor": 0,
@@ -10,10 +9,10 @@
"cells": [
{
"cell_type": "heading",
- "level": 2,
+ "level": 1,
"metadata": {},
"source": [
- "Chapter 5: Matter Waves"
+ "Chapter 5: The Schrodinger Equation"
]
},
{
@@ -21,203 +20,44 @@
"level": 2,
"metadata": {},
"source": [
- "Example 5.1, page no. 154"
+ "Example 5.2 Page 150"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
- "\n",
- "\n",
- "#Variable declaration\n",
- "\n",
- "h = 6.63 * 10 ** -34 #Planck's constant (J.s)\n",
- "m = 0.14 #mass of the baseball (kg)\n",
- "v = 27.0 #speed of the baseball (m/s)\n",
- "\n",
- "#Calculation\n",
- "\n",
- "lamda = h / (m * v)\n",
- "\n",
- "#Result\n",
- "\n",
- "print \"The de Broglie wavelength of the baseball is\",round(lamda/10**-34,2),\"X 10^-34 m.\""
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "output_type": "stream",
- "stream": "stdout",
- "text": [
- "The de Broglie wavelength of the baseball is 1.75 X 10^-34 m.\n"
- ]
- }
- ],
- "prompt_number": 3
- },
- {
- "cell_type": "heading",
- "level": 2,
- "metadata": {},
- "source": [
- "Example 5.2, page no. 154"
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "\n",
+ "#initiation of variable\n",
+ "#parta\n",
+ "from math import pi, sin\n",
"import math\n",
- "\n",
- "#Variable declaration\n",
- "\n",
- "h = 6.63 * 10 ** -34 #Planck's constant (J.s)\n",
- "me = 9.11 * 10 ** -31 #mass of electron (kg)\n",
- "q = 1.6 * 10 ** -19 #charge of electron (C)\n",
- "V = 50 #potential difference (V)\n",
- "\n",
- "#Calculation\n",
- "\n",
- "lamda = h / math.sqrt(2*me*q*V)\n",
- "\n",
- "#Result\n",
- "\n",
- "print \"The de Broglie wavelength of electron is\",round(lamda/10 ** -10,1),\"X 10^-10 m.\""
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "output_type": "stream",
- "stream": "stdout",
- "text": [
- "The de Broglie wavelength of electron is 1.7 X 10^-10 m.\n"
- ]
- }
- ],
- "prompt_number": 6
- },
- {
- "cell_type": "heading",
- "level": 2,
- "metadata": {},
- "source": [
- "Example 5.3, page no. 158"
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "\n",
- "\n",
- "#Variable declaration\n",
- "\n",
- "h = 6.63 * 10 ** -34 #Planck's constant (J.s)\n",
- "lamda = 1.0 * 10 ** -10 #de Broglie wavelength of the neutron (m)\n",
- "mn = 1.66 * 10**-27 #mass of neutrons (kg)\n",
- "e = 1.602 * 10 **-19 #charge of electron(C)\n",
- "\n",
- "#Calculation\n",
- "\n",
- "p = h / lamda\n",
- "K = p**2/(2*mn)\n",
+ "from scipy import integrate\n",
+ "h=1.05*10**-34;m=9.11*10**-31;L=10.0**-10; # all the values are taken in SI units\n",
+ "E1=h**2*pi**2/(2*m*L**2); E2=4*E1; #Energies are calculated\n",
+ "delE=(E2-E1)/(1.6*10**-19); #Difference in energy is converted to eV\n",
"\n",
"#result\n",
+ "print \"Energy to be supplied in eV. is \",round(delE,3);\n",
"\n",
- "print \"The kinetic energy is\",round(K/e,4),\"eV.\""
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "output_type": "stream",
- "stream": "stdout",
- "text": [
- "The kinetic energy is 0.0826 eV.\n"
- ]
- }
- ],
- "prompt_number": 8
- },
- {
- "cell_type": "heading",
- "level": 2,
- "metadata": {},
- "source": [
- "Example 5.8, page no. 177"
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "\n",
- "#Variable Declaration\n",
- "\n",
- "h = 1.05 * 10 ** -34 #(J.s)\n",
- "dx = 15 #length of the room (m)\n",
- "m = 0.1 #mass of the ball (kg)\n",
- "vx = 2.0 #velocity of the ball (m/s)\n",
- "\n",
- "#Calculation\n",
- "\n",
- "dpx = h /( 2* dx)\n",
- "dvx = dpx /m\n",
- "uncertainity = dvx/vx\n",
- "\n",
- "#Result\n",
- "\n",
- "print \"The relative uncertainty is\",round(uncertainity/10**-35,1),\"X 10^-35 which is not measurable.\""
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "output_type": "stream",
- "stream": "stdout",
- "text": [
- "The relative uncertainty is 1.8 X 10^-35 which is not measurable.\n"
- ]
- }
- ],
- "prompt_number": 12
- },
- {
- "cell_type": "heading",
- "level": 2,
- "metadata": {},
- "source": [
- "Example 5.9, page no. 178"
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "\n",
- "import math\n",
+ "#partb\n",
+ "x1=0.09*10**-10;x2=0.11*10**-10 #limits of the given region\n",
+ "def integrand(x,L):\n",
+ " return 2.0/L*(sin(pi*x/L))**2\n",
"\n",
- "#Variable declaration\n",
+ "probGnd=integrate.quad(integrand,x1,x2,args=(L))\n",
"\n",
- "h = 6.58 * 10 ** -16 #(eV.s)\n",
- "dx = 1.0 * 10 ** -14 / 2.0 # dx is half the length of confinement (m)\n",
- "c = 3.00 * 10 ** 8 #speed of light (m/s)\n",
- "me = 9.11 * 10 ** -31 # mass of electron (kg)\n",
- "e = 1.6 * 10 ** -19 #charge of electron (C)\n",
+ "#result\n",
+ "print \"The percentage probability of finding an electron in the ground state is \\n\",round(probGnd[0]*100,3);\n",
"\n",
- "#Calculation\n",
+ "#partc\n",
+ "k1=0.0;k2=0.25*10**-10;\n",
+ "def integrand(k,L):\n",
+ " return 2.0/L*(sin(2*pi*k/L))**2\n",
"\n",
- "dpx = h * c / (2 * dx)\n",
- "E = math.sqrt(dpx**2 + (me * c**2/e)**2)\n",
- "K = E - (me * c**2/e)\n",
+ "probExc=integrate.quad(integrand,k1,k2,args=(L))\n",
"\n",
"#result\n",
- "\n",
- "print \"The kinetic energy of an intranuclear electron is\",round(K/10**6,2),\"MeV.\""
+ "print \"The probability of finding an electron in the excited state is\",round(probExc[0],3);"
],
"language": "python",
"metadata": {},
@@ -226,67 +66,22 @@
"output_type": "stream",
"stream": "stdout",
"text": [
- "The kinetic energy of an intranuclear electron is 19.23 MeV.\n"
+ " Energy to be supplied in eV. is 111.978\n",
+ "The percentage probablility of finding an electron in the ground state is \n",
+ "0.383\n",
+ "The probablility of finding an electron in the excited state is 0.25\n"
]
}
],
- "prompt_number": 14
- },
- {
- "cell_type": "heading",
- "level": 2,
- "metadata": {},
- "source": [
- "Example 5.10, page no. 178"
- ]
+ "prompt_number": 7
},
{
"cell_type": "code",
"collapsed": false,
- "input": [
- "\n",
- "\n",
- "import math\n",
- "\n",
- "#Variable declaration\n",
- "\n",
- "dt = 1.0 * 10 ** -8 #lifetime (s)\n",
- "\n",
- "#calculation\n",
- "\n",
- "df = 1/(4*math.pi*dt)\n",
- "\n",
- "#result\n",
- "\n",
- "print \"The frequency of the light emitted is\",round(df/10**6,1),\"X 10^6 Hz.\"\n",
- "\n",
- "#Variable declaration\n",
- "\n",
- "c = 3.0 * 10 ** 8 #speed of light (m/s)\n",
- "lamda = 500 * 10 ** -9 #wavelength (m)\n",
- "\n",
- "#Calculation\n",
- "\n",
- "f = c/ lamda\n",
- "df_by_f0 = df / f\n",
- "\n",
- "#result\n",
- "\n",
- "print \"The fractional broadening is\",round(df_by_f0/10**-8,1),\"X 10^-8.\""
- ],
+ "input": [],
"language": "python",
"metadata": {},
- "outputs": [
- {
- "output_type": "stream",
- "stream": "stdout",
- "text": [
- "The frequency of the light emitted is 8.0 X 10^6 Hz.\n",
- "The fractional broadening is 1.3 X 10^-8.\n"
- ]
- }
- ],
- "prompt_number": 19
+ "outputs": []
}
],
"metadata": {}
generated by cgit (git 2.34.1) at 2024-12-20 18:38:31 +0000