%
%  w09step.m -- (djm:  02 mar 2004)
%    - eigenvalues for step well
%

clear

%  coordinates
L = 4;  mu2 = 4;
dl = 1/200;
lam2 = 1+dl:dl:mu2-dl;

btan = tan(sqrt(mu2-lam2)*L);
bt0 = btan./(abs([diff(btan) 0])<20);
bcot = -cot(sqrt(mu2-lam2)*L);
bc0 = bcot./(abs([diff(bcot) 0])<20);

%  plot
figure(1);  clf
plot(lam2,bt0,'b')
hold on
plot(lam2,bc0,'k')
plot(lam2,sqrt(lam2-1)./sqrt(mu2-lam2),'r')
axis([1 mu2 0 6])

title('\bf step-well eigenvalues')
ylabel('\bf tan & cot vs \surd{(\lambda^2-1)/(\mu^2-\lambda^2)}')
xlabel('\bf \lambda-axis')