GraphingCalculator 4;
Window 45 14 859 1334;
PaneDivider 438;
FontSizes 18;
StackPanes 1;
2D.Scale 0.25 2.5 1 1;
2D.BottomLeft -54.6875 -0.546875;
Text "Finite square well energies normalized to those of the infinite well.  x is the dimensionless energy E/E_1 (E_1 is the ground state of the infinite well) and v_0 = V_0/E_1 is the dimensionless barrier height.";
Color 2;
MathPaneSlider 10;
Expr v_0=slider([0,100,100]);
Text "Even eigenstates:";
Color 17;
Expr tan([pi/2*sqrt(x)]);
Color 17;
Expr sqrt([v_0/x]-1),x>0;
Color 17;
Expr x=m^2,in(m,set(1,3,5,7,9,11));
Color 17;
Expr tan([pi/2*sqrt(x)])-sqrt([v_0/x]-1),x>0;
Text "Or write this way:";
Expr sqrt(x)*tan([pi/2*sqrt(x)]);
Color 3;
Expr sqrt(v_0-x),x>0;
Color 17;
Expr sqrt(x)*tan([pi/2*sqrt(x)])-sqrt(v_0-x),x>0;
Text "Odd eigenstates.   p flips both terms upside-down to make them easier to see and compare to even case.";
Color 6;
Expr p=slider([-1,1,1]);
Color 17;
Expr p*cot([pi/2*sqrt(x)]);
Color 17;
Expr -(p*sqrt([v_0/x]-1)),x>0;
Color 17;
Expr x=m^2,in(m,set(2,4,6,8,10,12));
Text "Or this version:";
Color 5;
Expr p*sqrt(x)*cot([pi/2*sqrt(x)]);
Color 17;
Expr -(p*sqrt(v_0-x)),x>0;
Text "The energies of the infinite well are E_m = n^2*E_1, so in dimensionless variables:";
Expr function(E,m)=m^2;
Color 17;
Expr x=function(E,m),in(m,set(1*ldots*20));