Abstract
This is a study of the sum zeta (s; alpha ) identical to Ej=1infinity (Ej( alpha ))-s over the eigenvalues Ej( alpha ) of Schrodinger's equation in a (billiard) domain D with reflecting walls, threaded by a single line of magnetic flux alpha . For integer s, zeta (s; alpha ) is calculated by generalising a Green function technique of Itzykson et al. (ibid., vol.19, L111-5, 1986) based on a conformal transformation between D and the unit disc. When the transformation is generated by a polynomial of finite degree an explicit formula enables zeta (2; alpha ) to be easily computed with high accuracy. In conjunction with a semiclassical approximation the exact values of zeta (2; alpha ) can be used to calculate the ground state E1( alpha ) for a non-integrable billiard, with an error of about one per cent.
Published Version
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call