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{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Chapter 5: The Schrodinger Equation"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Example 5.1: Displacement_and_velocity_of_the_object.sce"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"clear \n",
"clc\n",
"disp('Exa-5.1');//The solution involves very complex symbolic equation solving and approximations. Hence only answers are displayed\n",
"printf('The displacement and velocity of the ball are found out in 2 steps\n step1-before reaching the surface of water and \n step2-Inside water till it rises back to surface\n');\n",
"printf('The values are as follows: v1(t)=-g*t and y1(t)=H-((g/2)*t^2))\n');\n",
"printf('In region 2: v2(t)=(-B/m*sqrt(2*H/g))+(B/m-g)*t; y2(t)= H+ HB/mg -B/m*sqrt(2*H/g)+ (B/m-g)');"
]
}
,
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Example 5.2: Solution_for_a_and_b.sce"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"clear \n",
"clc\n",
"disp('Exa-5.2(a)');\n",
"h=1.05*10^-34;m=9.11*10^-31;L=10^-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",
"printf('Energy to be supplied is %.0f eV.\n',delE);\n",
"disp('Exa-5.2(b)');\n",
"x1=0.09*10^-10;x2=0.11*10^-10 //limits of the given region\n",
"probGnd=(2/L)*integrate('(sin(%pi*x/L)^2)','x',x1,x2);\n",
"printf('The percentage probablility of finding an electron in the ground state is %.2f.\n',probGnd*100);\n",
"disp('Exa-5.2(c)');\n",
"x1=0,x2=0.25*10^-10;\n",
"probExc=(2/L)*integrate('(sin(2*%pi*x/L)^2)','x',x1,x2);\n",
"printf('The probablility of finding an electron in the excited state is %.2f.\n',probExc);"
]
}
,
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Example 5.3: Proof_for_average_value_of_x.sce"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"clear \n",
"clc\n",
"disp('Ex-5.3');\n",
"x1=0;x2=L;\n",
"xavg=(2/L)*integrate('sin(%pi*x/L)^2','x',x1,x2);\n",
"printf('The average value of x is found out to be L/2 which apparently is independent of Qunatum state.');"
]
}
],
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"display_name": "Scilab",
"language": "scilab",
"name": "scilab"
},
"language_info": {
"file_extension": ".sce",
"help_links": [
{
"text": "MetaKernel Magics",
"url": "https://github.com/calysto/metakernel/blob/master/metakernel/magics/README.md"
}
],
"mimetype": "text/x-octave",
"name": "scilab",
"version": "0.7.1"
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|
