Asymptotics of the eigenvalues of the rotating harmonic oscillator

DOI10.1016/S0377-0427(98)00070-3zbMath0928.34063MaRDI QIDQ1298538

T. M. Dunster

Publication date: 12 January 2000

Published in: Journal of Computational and Applied Mathematics (Search for Journal in Brave)

zbMATH Keywords

solutionsSchrödinger equationturning point theoryWKB methods

Mathematics Subject Classification ID

Particular ordinary differential operators (Dirac, one-dimensional Schrödinger, etc.) (34L40) 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) Singular perturbations, turning point theory, WKB methods for ordinary differential equations (34E20) Asymptotic distribution of eigenvalues, asymptotic theory of eigenfunctions for ordinary differential operators (34L20)

Related Items (6)

Simplified Asymptotic Solutions of Differential Equations Having Two Turning Points, with an Application to Legendre Functions ⋮ Uniform asymptotic expansions for Laguerre polynomials and related confluent hypergeometric functions ⋮ On the Borel summability of WKB solutions of certain Schrödinger-type differential equations ⋮ Computation of asymptotic expansions of turning point problems via Cauchy's integral formula: Bessel functions ⋮ Olver's error bound methods applied to linear ordinary differential equations having a simple turning point ⋮ Liouville-Green expansions of exponential form, with an application to modified Bessel functions

Cites Work

• Unnamed Item
• On the theory of vibration-rotation interaction
• Asymptotic solutions of second-order linear differential equations having almost coalescent turning points, with an application to the incomplete gamma function
• The rotating harmonic oscillator eigenvalue problem. I. Continued fractions and analytic continuation
• Application of a New Mathematical Method to Vibration-Rotation Interaction
• A Note on the Theory of Vibration-Rotation Interaction

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