Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Quantum mechanics

  1. Nov 6, 2007 #1
    1. The problem statement, all variables and given/known data

    Determine the energy levels, their degeneracy and wave functions (in ket notation) of a particle with spin quantum number s =1 if the Hamiltonian is [itex]AS_x^2 + AS_y^2 + B S_z^2[/itex] where A and B are constants.

    3. The attempt at a solution'

    I've spent ages thinking about this but I keep finding that the Hamiltonian is [itex](\hbar^2/4)(2A + B)I[/itex] where I is the identity matrix. This is very strange since it implies that there are an infinite number of eigenstates with identically the same eigenvalue!
     
  2. jcsd
  3. Nov 6, 2007 #2

    malawi_glenn

    User Avatar
    Science Advisor
    Homework Helper

    What matrices did you use for the S_x etc? Not the pauli matrices right? They are only valid for spin 1/2 partilces.
     
  4. Nov 6, 2007 #3

    clem

    User Avatar
    Science Advisor

    [itex]AS_x^2 + AS_y^2 + B S_z^2=AS^2+(B-A)S_z^2.[/itex]
    You know S^2. There are three values of S_z, and two of S_z^2.
    You don't need to know any matrices.
     
  5. Nov 6, 2007 #4
    Hi clem and malawi_glenn,

    Thanks heaps for pointing out my mistake.
     
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook