I'm trying to write a normalised wavefunction at time t, given the normalised wavefunction at t=0. I've found out that first I should write the initial wavefunction as a sum of the energy eigenfunctions, and then as time evolves, each term gets multiplied by e^(-i*E_n*t/hbar) where E_n is the eigenenergy of the eigenfunction.
Given that the eigenfunction is
sqrt(2/L)*sin(n*Pi*x/L)
how do I find the eigenenergy?