(adsbygoogle = window.adsbygoogle || []).push({}); [SOLVED] Functions, operator => eigenfunction, eigenvalue

1. The problem statement, all variables and given/known data

Show, that functions

f1 = A*sin([tex]\theta[/tex])exp[i[tex]\phi[/tex]] and

f2 = B(3cos[tex]^{2}[/tex]([tex]\theta[/tex]) - 1) A,B - constants

are eigenfunctions of an operator

and find eigenvalues

3. The attempt at a solution

This is what i got for the first function:

The next step is to solve left part of the equation, and than compare it to the right part.

The question arises, how to solve that equation?

I tried simplifying left part of an equation in mathcad, and I got

Next question from that part, is if I am doing it right, how to compare those parts, and answer a question - weather this function is an eigenfunction of an operator?

Thank You in advance, and I am constantly near computer and waiting for suggestions.

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# Functions, operator => eigenfunction, eigenvalue

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