|MadSci Network: Chemistry|
Off hand I didn't know the answer so I poked around. I remembered something like this on my graduate exam so here is the short answer. I think this will give you what you want if not let me know.
Wavefunction overlap 1D particle in a box (the equation is given on the website)
Quoted from the website:
"You can easily show that the overlap of different wavefunctions is necessarily zero. Consider, for example, if øm and øn have different symmetries their product will be antisymmetric and the integral will vanish. Different arguments are required for wavefunctions of the same symmetry type, but the result is the same. S = 0 if 'm' and 'n' are different.
We indicate the 'no overlap' property of wavefunctions by saying they are 'orthogonal.' Valid wavefunctions with different quantum numbers must always be orthogonal.
Note that a wavefunction can never be orthogonal to itself. Setting m = n makes the overlap integral identical to the normalization integral, i.e., Smm = 1."
Also some handy references:
Physical Chemistry, 7th Edition, Peter Atkins and Julio de Paula Applied Mathematics for Physical Chemistry by James R. Barrante
Try the links in the MadSci Library for more information on Chemistry.