On the nature of energy levels of anharmonic oscillators

DOI10.1006/aphy.1998.5902zbMath0930.34075OpenAlexW1994126538MaRDI QIDQ1301810

L. V. Chebotarev

Publication date: 9 February 2000

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

Full work available at URL: https://doi.org/10.1006/aphy.1998.5902

zbMATH Keywords

complex turning pointsenergy levelsanharmonic oscillatorsBohr-Sommerfeld formulaequivalent scatteringquantum reflectionsquartic, sextic, octic, and decadic oscillatorsStokes points

Mathematics Subject Classification ID

Particular ordinary differential operators (Dirac, one-dimensional Schrödinger, etc.) (34L40) Dynamical systems in other branches of physics (quantum mechanics, general relativity, laser physics) (37N20) Semiclassical techniques, including WKB and Maslov methods applied to problems in quantum theory (81Q20) (2)-body potential quantum scattering theory (81U05) Singular perturbations, turning point theory, WKB methods for ordinary differential equations (34E20) Qualitative investigation and simulation of ordinary differential equation models (34C60) Scattering theory, inverse scattering involving ordinary differential operators (34L25)

Related Items (4)

Energy levels of one-dimensional anharmonic oscillator via neural networks ⋮ Zero-point energies of subharmonic oscillators ⋮ Perturbation theory in a framework of iteration methods ⋮ Arnold's potentials and quantum catastrophes

Cites Work

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• Summation of divergent series by order dependent mappings: Application to the anharmonic oscillator and critical exponents in field theory
• Second-order linear differential equations with two turning points
• The summation of the ordinary and renormalized perturbation series for the ground state energy of the quartic, sextic, and octic anharmonic oscillators using nonlinear sequence transformations
• The spectrum of the quartic oscillator
• Error bounds for the Bohr - Sommerfeld formula
• Flat resonances in one-dimensional quantum scattering
• The Two-Minima Problem and the Ammonia Molecule

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