Calculating Expectation Value for E in Wavefunction

[jaejoon89]

I'm trying to check that the expectation value <E> is E for the wavefunction

sqrt(2/L) sin(2pix / L)

I know the shortcut way of doing it by saying that the hamiltonian multiplied by the function is just the eigenvalue E multiplied by the function, and since the function is normalized the answer is E. However, I want to try to check it:

But when I take the hamiltonian of the function (V=0) and then multiply that by the complex conjugate and integrate from 0 to L I get

2 h^2 / mL^2

which is not quite what I would expect if it equals E since I know for the 1D Schrödinger equation

E_n = n^2 h^2 / 8mL^2
=>E_2 = h^2 / 2mL^2

What's wrong?

 

[gabbagabbahey]

You must be integrating incorrectly, if you show your calculations, we can point out your error...