Exact and Quasiclassical Fredholm Solutions of Quantum Billiards
- 10 April 1995
- journal article
- research article
- Published by American Physical Society (APS) in Physical Review Letters
- Vol. 74 (15) , 2851-2854
- https://doi.org/10.1103/physrevlett.74.2851
Abstract
Quantum billiards are much studied as perhaps the simplest case which presents the central difficulty that the quasiclassical approximation is expressed as a divergent series. We find here, using the Fredholm method, an exact Green's function for billiards expressed as a ratio of absolutely convergent series. We make the quasiclassical approximation to this ratio. The method provides a convergence argument for previous results and an extension of results obtained for the spectrum to the full Green's function.Keywords
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