THE HURWITZ THEOREM FOR BESSEL FUNCTIONS AND ITS CONSEQUENCES FOR ANTIBOUND STATES


MICHAEL S P EASTHAM

mandh@chesilhay.fsnet.co.uk

Department of Computer Science
Cardiff University
PO Box 916, Cardiff CF24 3XF, UK






The Hurwitz theorem states (inter alia) that the Bessel function $ J_{-v}(ix)$ has no zeros for real $ x$ and $ 2N < v< 2N+1$ $ (N=0,1,...)$. We derive a number of consequences for the Dirichlet and Neumann antibound states concerning the Bessel and hypergeometric equations, in which the potential has only exponential decay $ \sim \exp (-2x)$ at infinity. Little is known about the distribution of resonances and antibound states for this decay, and a number of conjectures are suggested, supported by computational considerations.


EPSRC Gregynog Workshop, 21-26 July 2002

Gregynog Abstracts