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Dirac Notation for a Quantum State of a System

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In the dirac notation for a quantum state of a system, an eigenstate wave function u_n is replaced by the vector |n>, and a general state wave function (see attached)

a) Translate the following mathematical statements to the corresponding forms n wave mechanics: i) <n|m> = (see attached), where A is an hermitian operator.

b) By considering the expansion of (see attached) in terms of |n>, derive the following result which expresses the completeness property of the set of eigenstates.

(See attached)

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