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Text "Bohr Model Hydrogenic Energy Levels and Classical Potential 

Version 0.1 11-7-09

To do:
(i) 

Ground state energy; energy levels of hydrogenic atoms (in eV):";
Color 7;
Expr Z=1;
Color 5;
Expr E_1=13.6;
Color 6;
Expr function(E,p)=[-Z^2]*E_1/p^2;
Text "Bohr radius (in Angstroms) and orbital radii:";
Color 5;
MathPaneSlider 24;
Expr a_0=slider([0,0.5]);
Color 8;
Expr function(R,m)=m^2*a_0/Z;
Text "Coulomb potential.   Note ke^2=2E1*a0.";
Color 3;
Expr function(V,x)=[-2]*E_1*a_0*Z/x;
Text "Effective potential for radial motion V(r)+l^2/2mr^2.   The quantization condition is l=p*hbar.  Note hbar^2/m=2E1*a0^2.   ";
Expr function(U,x,p)=function(V,x)+p^2*E_1*a_0^2/x^2;
Color 17;
Expr function(V,x),x>0;
Color 17;
Expr function(U,x,1),x>0;
Color 17;
Expr function(U,x,p),x>0,in(p,set(1,2,3,4,5));
Color 17;
Expr function(U,x,p),x>0,in(p,set(1,2,3,4,5,6,7,8,100));
Color 7;
Expr x=0;
Text "Classically forbidden regions:";
Color 7;
Expr x<0;
Color 17;
Expr y<function(V,x),x>0;
Color 7;
Expr y<function(U,x,1),x>0;
Text "Energy levels.  Radii of Bohr orbits are classical circular orbits of the same energy:";
Color 17;
Expr y=function(E,1),0<x<function(R,1);
Color 17;
Expr y=function(E,p),in(p,set(1,2,3,4,5,6,7,8,100));
Color 17;
Expr y=function(E,p),in(p,set(9,10,11,12,13,14,15,20,25,30,35,40,45,50,55));
Color 4;
Expr y=function(E,p),0<x<function(R,p),in(p,set(1,2,3,4,5,6,7,8,100));
Color 4;
Expr y=function(E,p),0<x<function(R,p),in(p,set(9,10,11,12,13,14,15,20,25,30,35,40,45,50,55));
Text "


<size=15>Author: David A. Craig <<http://web.lemoyne.edu/~craigda/>";