SUM-RULES FOR ZEROS OF BESSEL-FUNCTIONS AND AN APPLICATION TO SPHERICAL AHARONOV-BOHM QUANTUM BAGS

We study the sum zeta(H)(s) = SIGMA(j) E(j)-s over the eigenvalues E(j ) of the Schrodinger equation in a spherical domain with Dirichlet wal ls, threaded by a line of magnetic flux. Rather than using Green funct ion techniques, we tackle the mathematically non-trivial problem of fi nding exact sum rules for the zeros of Bessel functions J(nu), which a re extremely helpful when seeking numerical approximations to ground s tate energies. These results are particularly valuable if nu is neithe r an integer nor half an odd integer.