# Group Theory why transformations of Hamiltonian are unitary?

1. Nov 14, 2015

### applestrudle

This is what I have so far:

I'm trying to show that the matrix D has to be unitary. It is the matrix that transforms the wavefunction.

2. Nov 14, 2015

### HallsofIvy

The matrix that transforms the wave function how? So that it preserves some property? Transformations do NOT have to be unitary unless you are trying to lengths of vectors.

3. Nov 14, 2015

### applestrudle

In lectures we were showing
Tψ(r) = ψ(Ur) = ΣDij ψ(r)

Dij has to be unitary and form a representation of T - I'm just trying to figure out the proof. Are you saying this is only try if you scale the position vector r?