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

Operators in a three level system

  1. Sep 23, 2006 #1
    I'm having the worst time with a homework problem, in which I am asked to establish the operators which correspond to the independent observables of a three level system( states |1> , |0>,|-1> ) . I know that the operators should be 3x3 matrices, so I tried to express an arbitrary 3x3 Hermitian matrix in terms of a base set of 3x3 matrices, as it can be easily done with the 2 level system, where one gets the indentity operator and the 3 Pauli matrices. The thing is that I end up with the identity operaror and 9 more matrices! Even if this is correct, what are the observables which corespond to these matrices?

    Any help would be greatly appreciated.
     
  2. jcsd
  3. Sep 23, 2006 #2

    Meir Achuz

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    You can use the matrices for a spin one system.
     
  4. Sep 25, 2006 #3
    try the basis for SO(3).
     
  5. Sep 26, 2006 #4
    If you could show us these matrices we could have some suggestions.

    Michel
     
  6. Sep 29, 2006 #5

    reilly

    User Avatar
    Science Advisor

    First you have to determine what the operators are, and their commutation rules -- presumably. there's energy, and angular momentum, perhaps spin, perhaps momentum, .....

    Regards,
    Reilly Atkinson
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?



Similar Discussions: Operators in a three level system
  1. Two level system (Replies: 2)

Loading...