1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
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...