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.