I having trouble finding the eigenvalues and eigenfunctions for the operator(adsbygoogle = window.adsbygoogle || []).push({});

[tex]\hat{Q} = \frac{d^2}{d\phi^2}, [/tex]

where [tex]\phi[/tex] is the azimuthal angle. The eigenfunctions are periodical,

[tex]f(\phi) = f(\phi + 2\pi), [/tex]

which I think should put some restrictions on the eigenvalues.

I think that the eigenfunctions are complex exponentials, and that the eigenvalues are 0,-1,-2,..., but I am not sure if this is correct. Also I have to determine if the spectrum is degenerate, that is, if two (or more) distinct eigenfunctions correspond to the same eigenvalue.

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# Eigenvalues and -functions

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