% This is the function from p. 6 of the first infinite square well lecture.
% It is a delta function in the limit as N goes to infinity.
% Increase N and see what happens.
% The integral of this function is one, but numerically the area over the
% the range of the plot is slightly larger than one.

N = 1;
dx = 0.001;
x = (-10+dx/2):dx:(10-dx/2);

delta = sin(pi*(N + 0.5)*x)./(pi*x);

plot(x,delta)
area = trapz(x,delta)