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Armed with the braket formalism we can construct any operator
in Hilbert space. The projection operator P_{a} is defined
as
Note that
and in general any projection operator P has the property
P^{2}=P. Consider operator X whose eigenstates are given
by the set
.
If we
define the projection operators
P_{an} =  a_{n}><a_{n}, show that
operator X can be expressed as a sum of projection operators, i.e.

(1.38) 
Bernard Zygelman
19990921