Spectroscopy of drums and quantum billiards: perturbative and non-perturbative results

Details Spectroscopy of drums and quantum billiards: perturbative and non-perturbative results Spectroscopy of drums and quantum billiards: perturbative and non-perturbative results

2009-10-26

arxiv.org/abs/0910.4798v1

Physics

Quantum Physics

29 pages, 12 figures, 7 table

Scientific paper

We develop powerful numerical and analytical techniques for the solution of the Helmholtz equation on general domains. We prove two theorems: the first theorem provides an exact formula for the ground state of an arbirtrary membrane, while the second theorem generalizes this result to any excited state of the membrane. We also develop a systematic perturbative scheme which can be used to study the small deformations of a membrane of circular or square shapes. We discuss several applications, obtaining numerical and analytical results.

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