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Unformatted text preview: a set of orthonormal simultaneous eigenstates of both operators. We proved this for the case of operators with non-degenerate 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 (H ,H ,H ) ] whose simultaneous eigenstates are non-degenerate 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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This note was uploaded on 02/27/2012 for the course PHYSICS 3220 taught by Professor Stevepollock during the Fall '08 term at Colorado.
- Fall '08