There is a particle in a box from -a to a (i.e. length of box = 2a) with the following wavefunction:

ψ(x,0) = C(a²−x²) when |x| < a

ψ(x,0) = 0 when |x| > a

where C is a constant.

Find a value of C such that ψ(x,0) is normalised and hence write down the corresponding probability density.

To do this I tried ∫|ψ(x,0)|² = 1 from -a to a

= ∫ (ψ*(x,0) times ψ(x,0)) = C²(a²−x²)(a²−x²) and followed on from here.

Does this look right?