% This program sums the terms in the linear combination of eigenstates
% to produce a wave function that is constant for 0 < x < 0.5 and zero
% between 0.5 and 1.0 .
% It is describe in the notes of the last infinite square well lecture.

nterms = 100; % nterms is the number of terms kept.
             % Convergence should be attained as nterms becomes large.

n = 1:nterms;
c = (1 - cos(pi*0.5*n))*2./(pi*n); % coefficients computer in notes.

x = 0:0.001:1;

psi = 0*x;

for counter = 1:nterms,
   psi = psi + c(counter)*sqrt(2)*sin(pi*counter*x);
end

exactpsi = sqrt(2)*(x < 0.5);

plot(x,abs(psi).^2,x,abs(exactpsi).^2)
xlabel('x')
ylabel('|psi|^2')