Calculating Energy in a Quantum Chemistry System

[Knight]

There is an initial state Psi(x) =Ax(b/2 - x) when 0< x <b/2 and Psi(x) = 0 when b/2 < x <b

I have to find the second lowest value possibly be obtained in a measurement of the energy.

Should I treat this as a box with width b and possible energy states E=n^2*h^2/8mb^2 ? Or should I use the width b/2 ?

Could someone please help me?

 

[GCT]

How are you going to incorporate the wave equations?

 

[Knight]

Let me explain this problem better.
What I have to do is calculate the propability that the measured energy from this system is E2
O.K. So I have to find the Fourier coefficients, when I expand the initial state I mentioned above from 0 to b/2 in the eigenfunctions of the energy operator, or sqrt(2/b)*sin(n*pi*x/b). I know these eigenfunctions are derived from x=0 to x=b but Psi(x) =Ax(b/2 - x) is when 0< x <b/2
I am doing this the correct way or am I way off?