Classical Quantization of a Hamiltonian with Ergodic Behavior
- 21 July 1980
- journal article
- research article
- Published by American Physical Society (APS) in Physical Review Letters
- Vol. 45 (3) , 150-153
- https://doi.org/10.1103/physrevlett.45.150
Abstract
Conservative Hamiltonian systems with two degrees of freedom are discussed where a typical trajectory fills the whole surface of constant energy. The trace of the quantum mechanical Green's function is approximated by a sum over classical periodic orbits. This leads directly to Selberg's trace formula for the motion of a particle on a surface of constant negative curvature, and, when applied to the anisotropic Kepler problem, yields excellent results for all the energy levels.Keywords
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