# 3D unitary transformation

1. Aug 17, 2011

### newshurik

Hello,

I have a 3D complex wave function and I want to apply a unitary transformation to rotate it with respect to arbitrary axis.

Anybody have any ideas how I can do that?

Sasha

2. Aug 18, 2011

### PhilDSP

Last edited: Aug 18, 2011
3. Aug 20, 2011

### Bill_K

Does your wavefunction have a definite angular momentum, i.e. does it contain a spherical harmonic Ylm? If so, you rotate it using a rotation matrix Dlmm'. See a good book on Angular Momentum such as Edmonds.

4. Aug 21, 2011

### Jazzdude

Spatial rotations are generated by the angular momentum operators. So the general answer to your request is picking a representation of the angular momentum operators (Lx,Ly,Lz) and evaluating the operator exponential

exp(i*n.L) = exp(i*(nx*Lx+ny*Ly+nz*Lz))

for a vector (nx,ny,nz) that specifies the axis of rotation and the rotation angle by its magnitude.

In an angular momentum eigenbasis that is aligned with n that unitary operator is diagonal. So you might find expanding in that basis to be simpler than evaluating the most general operator exponential.

Cheers,

Jazz