Spectral Zeta Functions for Spherical Aharonov-Bohm Quantum Bags

Elizalde, E.; Leseduarte, S.; Romeo, A.

Spectral Zeta Functions for Spherical Aharonov-Bohm Quantum Bags

Authors

Elizalde, E.

Leseduarte, S.

Romeo, A.

Description

We study the sum $\dsζ_H(s)=\sum_j E_j^{-s}$ over the eigenvalues $E_j$ of the Schrdinger equation in a spherical domain with Dirichlet walls, threaded by a line of magnetic flux. Rather than using Green's function techniques, we tackle the mathematically nontrivial problem of finding exact sum rules for the zeros of Bessel functions $J_ν$, which are extremely helpful when seeking numerical approximations to ground state energies. These results are particularly valuable if $ν$ is neither an integer nor half an odd one.
15 pages, LaTeX file