Spectroscopy of drums and quantum billiards: Perturbative and nonperturbative results

Journal Article · Sat May 15 00:00:00 EDT 2010 · Journal of Mathematical Physics

DOI:https://doi.org/10.1063/1.3364792· OSTI ID:21335952

Amore, Paolo ^[1]

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1. Facultad de Ciencias, CUICBAS, Universidad de Colima, Bernal Diaz del Castillo, 340 Colima, Colima (Mexico)

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 arbitrary 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.

• OSTI ID: 21335952
• Journal Information: Journal of Mathematical Physics, Vol. 51, Issue 5; Other Information: DOI: 10.1063/1.3364792; (c) 2010 American Institute of Physics; Country of input: International Atomic Energy Agency (IAEA); ISSN 0022-2488
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
EQUATIONS
EXCITED STATES
GROUND STATES
MATHEMATICAL SOLUTIONS
M-THEORY
QUANTUM MECHANICS
SPECTROSCOPY