Archive for the ‘Quantum Mechanics’ Category

Liboff: “Introductory Quantum Mechanics”, 2nd edition p.86 exercise 3.16

Author: Panagiotis

2 Jan

The exercise [1, p. 86 ex. 3.16] asks to prove that if the eigenfunctions and eigenvalues of an operator $\widehat{A}$ are $\{\phi_{n}\}$ and $\{a_{n}\}$ , respectively ( $\ensuremath{\widehat{A}}\phi_{n}=a_{n}\phi_{n}$ ) then the eigenfunctions of a function $f(x)$ having an expansion of the form:

$f(x)=\sum\limits^{\infty}_{l=0}b_{l}x^{l}$

will also be $\phi_n$ with corresponding eigenvalues $f(a_n)$ , $n=0,1...$ . That is $f(\widehat{A})\phi_n=f(a_n)\phi_n$ . read the conclusion >

Filed under: Quantum Mechanics, Solved Problems

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