% This problem is similar to leftside.m except that the wavefunction
% is centered about 0.5 with width Delta on each side of 0.5.

nterms = 100; % Number of terms kept in the series.
Delta = 0.1;

n = 1:nterms;
c = 2*sin(0.5*n*pi).*sin(n*pi*Delta)./(pi*n)/sqrt(Delta);

x = 0:0.001:1;
psi = 0*x;

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

psi2exact = (x > (0.5 - Delta)).*(x < (0.5 + Delta))/(2*Delta);

plot(x,psi.^2,x,psi2exact)
xlabel('x')
ylabel('|psi|^2')