Zeros of eigenfunctions of some anharmonic oscillators

DOI10.5802/aif.2362zbMath1155.34043arXivmath-ph/0612039OpenAlexW1792727998MaRDI QIDQ931896

Andrei Gabrielov, Alexandre Eremenko, Boris Zalmanovich Shapiro

Publication date: 4 July 2008

Published in: Annales de l'Institut Fourier (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math-ph/0612039

zbMATH Keywords

eigenfunctionsdistribution of zerosmeromorphic functionssecond order differential operator

Mathematics Subject Classification ID

Particular ordinary differential operators (Dirac, one-dimensional Schrödinger, etc.) (34L40) Selfadjoint operator theory in quantum theory, including spectral analysis (81Q10) Asymptotic distribution of eigenvalues, asymptotic theory of eigenfunctions for ordinary differential operators (34L20)

Related Items (12)

Research questions on meromorphic functions and complex differential equations ⋮ Localization of the states of a \(PT\)-symmetric double well ⋮ High energy eigenfunctions of one-dimensional Schrödinger operators with polynomial potentials ⋮ DOUBLE WELL POTENTIAL: PERTURBATION THEORY, TUNNELING, WKB (BEYOND INSTANTONS) ⋮ One-dimensional quasi-exactly solvable Schrödinger equations ⋮ Asymptotics of eigenvalues of non-self-adjoint Schrödinger operators on a half-line ⋮ Analytic continuation of eigenvalues of a quartic oscillator ⋮ On the rational monodromy-free potentials with sextic growth ⋮ Entire functions of finite order as solutions to certain complex linear differential equations ⋮ Evolutionary branching via replicator-mutator equations ⋮ Potentials of the Heun class: The triconfluent case ⋮ The semiclassical small-ℏ limit of loci of roots of subdominant solutions for polynomial potentials

Cites Work

• Nevanlinna functions with real zeros
• High energy eigenfunctions of one-dimensional Schrödinger operators with polynomial potentials
• Normalizability of one-dimensional quasi-exactly solvable Schrödinger operators
• Quasi-exactly-solvable problems and sl(2) algebra
• Anharmonic oscillator and double-well potential: Approximating eigenfunctions
• A note on the zeros of solutions [wacute+P(z)w= 0 where P is a polynomial]
• Lie Algebras, Cohomology, and New Applications to Quantum Mechanics
• Lie-algebras and linear operators with invariant subspaces
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item

This page was built for publication: Zeros of eigenfunctions of some anharmonic oscillators