Particle in a Box/Wave function decomposition.

[spikethekitty]

Homework Statement

There is a particle in an infinite square well and the normalized wave function is divided into 3 parts. Psi = A between 0< x < L/3, B where L/3< x < 2L/3, and C from 2L/3 < x < L. I have to prove that the decomposition into psi_n yields a specific c_n.

Homework Equations

c_n= Integral psi^*Psi dx.

psi_n= Sqrt(2 / L) Sin(n pi x / L)

The Attempt at a Solution

I have already proven that the wave function is normalized. The only thing i am confused about is what i do about the integral. Since Psi is in three parts, I am pretty sure that I integrate A times psi_n in terms of x from 0 to L/3, instead of -infinity to infinity, and likewise for B and C. What i don't know is what to do after that. Do i add the three answers together or multiply them? or am i on the complete wrong track already?

 

[lfqm]

You must add the integrals, basic calculus:

(Integral from a to c) = (Integral from a to b) + (Integral from b to c)

If you didn't use this, how did you prove the function was normalized?