348-problem10 - Chem. 540 Instructor: Nancy Makri PROBLEM...

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Unformatted text preview: Chem. 540 Instructor: Nancy Makri PROBLEM 10 ˆ ˆ The operator f ( A) , where A is an operator and f is any function, is defined by the Taylor series expansion of the function. For example, ˆ eA ≡ ∞ 1 ˆ ∑ k !Ak . k =0 ˆ Show (in general) that if a is an eigenstate of A with eigenvalue λ , then a is also an eigen ˆ state of the operator f ( A) . Find the latter’s eigenvalue. ...
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