Exact sum rules for quantum billiards of arbitrary shape

Journal Article · Mon Jan 15 04:00:00 EST 2018 · Annals of Physics

DOI:https://doi.org/10.1016/J.AOP.2017.11.003· OSTI ID:22848270

Amore, Paolo ^[1]

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

Highlights: Sum rules of order one for domains of arbitrary shape are considered. The sum rules are proved to be finite. Exact expressions for number of examples are obtained. These expressions are verified with accurate numerical tests. -- Abstract: We have derived explicit expressions for the sum rules of order one of the eigenvalues of the negative Laplacian on two dimensional domains of arbitrary shape. Taking into account the leading asymptotic behavior of these eigenvalues, as given from Weyl’s law, we show that it is possible to define sum rules that are finite, using different prescriptions. We provide the explicit expressions and test them on a number of non trivial examples, comparing the exact results with precise numerical results.

• OSTI ID: 22848270
• Journal Information: Annals of Physics, Journal Name: Annals of Physics Vol. 388; ISSN 0003-4916; ISSN APNYA6
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
ASYMPTOTIC SOLUTIONS
COMPARATIVE EVALUATIONS
EIGENVALUES
LAPLACIAN
SUM RULES
TWO-DIMENSIONAL SYSTEMS