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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

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    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.

  6. Sep 29, 2006 #5


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

    Reilly Atkinson
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