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Unformatted text preview: Chem. 540
Instructor: Nancy Makri PROBLEM 10
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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- Fall '08