% The solutions to the PIB with finite potential.
% x= ka/2  y = Ka/2  
% need m, e Vnot 
hbar = 1e-34 % J-sec
a = 1e-9 % meters
me = 1e-30 % kg;
E1 =  (hbar*pi/a)^2/(2*me)
Vo = 1.20e-18 ; % J;
n= sqrt(Vo/E1)
c = (pi/2)*sqrt(Vo/E1)
x = linspace(0,c,2000);
y = x.*tan(x);
z = sqrt(c^2-x.^2);
xp = x/(pi/2);
[v,Index] = find ( (diff(sign(y-z))) > 1)
plot(xp,y,xp,z,xp(Index),z(Index),'g*')
set(gca,'xlim',[0 1.1*c/(pi/2)],'ylim',[0 1.1*c])
xlabel('k*a/2 / [\pi/2]')
ylabel('\kappa*a/2')
% the solutions occur when z = y
% want xp(Index)