3D unitary transformation

  1. 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?

  2. jcsd
  3. 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!
    Last edited: Aug 18, 2011
  4. Bill_K

    Bill_K 4,157
    Science Advisor

    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.
  5. 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.


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