Spectral Zeta Functions of a 1D Schrödinger Problem

DOI10.1142/S140292511250026XzbMath1256.81040arXiv1110.2004MaRDI QIDQ3165455

Joe Watkins

Publication date: 26 October 2012

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

Full work available at URL: https://arxiv.org/abs/1110.2004

zbMATH Keywords

hypergeometric seriesintegrals of motionspectral zeta functions

Mathematics Subject Classification ID

Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics (81Q05) Selfadjoint operator theory in quantum theory, including spectral analysis (81Q10) Selberg zeta functions and regularized determinants; applications to spectral theory, Dirichlet series, Eisenstein series, etc. (explicit formulas) (11M36) Generalized hypergeometric series, ({}_pF_q) (33C20) Nonselfadjoint operator theory in quantum theory including creation and destruction operators (81Q12)

Cites Work

• The coherent potential method in the diffusion problem on a random substitution lattice
• {\cal PT} symmetry breaking and exceptional points for a class of inhomogeneous complex potentials
• Ten Physical Applications of Spectral Zeta Functions
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