I've got a problem that is to calculate the normalisation constant and then the probability of obtaining an energy measurement of [tex]E_n[/tex] for an infinite square well.

I often find out that I have made a mistake along the way which has made the problem ten times more complicated than it should be. In this case I have about a page of calculations, and even if I was doing it the right way, there could easily be an error in there somewhere that would be problematic for me. I was wondering if there was a way to check the answer.

The initial wave function is

[tex]\Psi(x,t=0)=A(a^2-x^2)[/tex]

for a square well from -a to a, where A is the normalisation constant.

and my Probability is

[tex]P_n=\frac{15}{n^2\pi^2a^4}(\frac{4a^2}{n^2\pi^2}+(-1)^{(n-1)}\frac{4a}{n\pi}+1)[/tex]

when n is odd, and [tex]P_n=0[/tex] when n is even

Apart from anything else, this seems extremely complicated for such a simple wave function, so I am inclined to think I've made a mistake. Can anyone help me figure out if I need to go back and start from scratch? If need be I can post all my workings out, but being so long it will take a little while to type up, so I will only post it if requested. Thank you.