Coaxial Cylinder-Aharonov-Bohm effect

aurelio

Hi Everyone,

I'm trying to find the eigenfunctions and eigenvalues for a quantum spinless particle within two concentric cylinders of radius \rho_a and \rho_b
, where \rho_a is less than\rho_b, with Dirichlet boundary conditions at these two radii. It's clear to me what the solution is for the case of \rho_a being equal to zero. The radial solution is the Bessel Function of order zero but how can I find the solution when \rho_a is finite.
IF I know what is the spectrum for this problem then I think I can determine what is the spectrum when there is a constant magnetic field B along the z direction only within the inner cylinder.
Please help