3D unitary transformation

by newshurik
Tags: complex function, gell-mann matrices, group theory, su3
newshurik is offline
Aug17-11, 09:35 AM
P: 5

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?

Phys.Org News Partner Physics news on Phys.org
A 'quantum leap' in encryption technology
Using antineutrinos to monitor nuclear reactors
Bake your own droplet lens
PhilDSP is offline
Aug18-11, 03:20 PM
P: 563
Hi Sasha,

You might want to look up information on the Schrödinger-Bloch equation or Schrödinger equation associated with a Bloch sphere rotation. Here's a paper you might find useful:

Quantum-to-Classical Correspondence and Hubbard-Stratonovich Dynamical
Systems, a Lie-Algebraic Approach - Victor Galitski



Don't miss the picture on page 12!
Bill_K is offline
Aug20-11, 06:29 PM
Sci Advisor
Bill_K's Avatar
P: 3,864
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.

Jazzdude is offline
Aug21-11, 04:14 PM
P: 178

3D unitary transformation

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.



Register to reply

Related Discussions
Unitary Transformation Problem Calculus & Beyond Homework 2
Finding unitary transformation Calculus & Beyond Homework 1
Unitary transformation Quantum Physics 5
unitary coordinate transformation = rotation? Calculus & Beyond Homework 2
about symmetry operation and a corresponding unitary transformation Quantum Physics 4