Multidimensional extension of a Wentzel–Kramers–Brillouin improvement for spherical quantum billiard zeta functions

DOI10.1063/1.530942zbMath0867.11060OpenAlexW1963626213MaRDI QIDQ4873258

August Romeo

Publication date: 10 August 1997

Published in: Journal of Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1063/1.530942

zbMATH Keywords

Dirichlet boundary conditionszeta functionwave functionquantum billiardsWKB approximationsresidues of the spectral zeta function poles

Mathematics Subject Classification ID

Semiclassical techniques, including WKB and Maslov methods applied to problems in quantum theory (81Q20) Other Dirichlet series and zeta functions (11M41) Miscellaneous applications of number theory (11Z05) Fixed points and periodic points of dynamical systems; fixed-point index theory; local dynamics (37C25) Determinants and determinant bundles, analytic torsion (58J52)

Related Items (4)

Quantum three-body system in D dimensions ⋮ Approximate series solutions of the \(N\)-dimensional position-dependent mass Schrödinger equation ⋮ Exact solutions of the position-dependent mass Schrödinger equation in \(D\) dimensions ⋮ EXACTLY SOLVABLE EFFECTIVE MASS D-DIMENSIONAL SCHRÖDINGER EQUATION FOR PSEUDOHARMONIC AND MODIFIED KRATZER PROBLEMS

Cites Work

• Sum rules for quantum billiards
• Comment on 'sum rules for quantum billiards'
• Zeta function of the Bessel operator on the negative real axis
• Sum rules for zeros of Bessel functions and an application to spherical Aharonov-Bohm quantum bags

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