# Operators in a three level system

1. Sep 23, 2006

### dantypas

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. Sep 23, 2006

### Meir Achuz

You can use the matrices for a spin one system.

3. Sep 25, 2006

### Epicurus

try the basis for SO(3).

4. Sep 26, 2006

### lalbatros

If you could show us these matrices we could have some suggestions.

Michel

5. Sep 29, 2006

### reilly

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