- #1
broegger
- 257
- 0
I having trouble finding the eigenvalues and eigenfunctions for the operator
where [tex]\phi[/tex] is the azimuthal angle. The eigenfunctions are periodical,
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.
[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.