How to Determine Energy Probabilities in an Infinite Potential Well?

[Firben]

Homework Statement

The wave function for a particle in a infinitely deep potential well is at some point in time Φ(x) = Nx(a-x). In which probability gives the energy measurment a another value than E₁ ,etc ground state

Homework Equations

1 = |c_n|^2 = |<Φ_n|Ψ>|^2 (1)

The Attempt at a Solution

[/B]
If Ψ_n(x) = sqrt(2/a)sin(n*(pi)*x/a) be the eigenfunction and put it into (1) and integrate. Is this right method I am doing ?

 

[blue_leaf77]

What are you asked to do in this problem? Initially I supposed you have to calculate the expansion coefficient, but equation (1) indicate that it's equal to unity (which is not correct either). Is it the N in $\Phi(x)$ that is asked? In that case simply use the requirement of normalization.