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### Projection operators

Armed with the bra-ket formalism we can construct any operator in Hilbert space. The projection operator Pa is defined as

 Pa = | a>

Note that and in general any projection operator P has the property P2=P. Consider operator X whose eigenstates are given by the set . If we define the projection operators Pan = | an><an|, show that operator X can be expressed as a sum of projection operators, i.e.

 (1.38)

Bernard Zygelman
1999-09-21