# Schrodinger Equation Preserves Normalization

1. Oct 15, 2008

### Kreizhn

1. The problem statement, all variables and given/known data
Show that the time dependent Schrodinger equation preserves the normalization of the wavefunction

2. The attempt at a solution
I don't need help showing this, I'm just not too sure what the question is asking. Do I just show that if a normalized wave-function $\psi$ is a solution to the TDSE, then the TDSE doesn't change the normalization? That is, assuming that U(t) is the time evolution operator $U(t) = \displaystyle e^{-\frac{i}{\hbar} Ht }$ do I just show that $\int_V |U(t) \psi|^2 dV$ is also normalized? (which should follow pretty easily since U(t) is unitary).