Unformatted text preview: a set of orthonormal simultaneous eigenstates of both operators. We proved this for the case of operators with nondegenerate states, but it is also true when there are degeneracies. (We will show below that when operators do not commute, it is impossible to find simultaneous eigenstates.) Claim: If N quantum numbers [example: (n x , n y , n z )] are required to uniquely specify a state, then there must exit N commuting operators [example: x y z ˆ ˆ ˆ (H ,H ,H ) ] whose simultaneous eigenstates are nondegenerate and whose N eigenvalues provide the quantum numbers that uniquely label the state. Such a set of operators is called a complete set of commuting operators (CSCO). We will give a proof later, when we talk about matrix formulation of QM....
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 Fall '08
 STEVEPOLLOCK
 NZ, simultaneous eigenstates

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