Asymptotic (semiclassical) equivalence for Schrödinger equations with singular potentials and for related systems of two first-order equations

DOI10.1063/1.530081zbMath0780.34056OpenAlexW2094769250MaRDI QIDQ3141341

Simonetta Cavall, Vincenzo Aquilanti, Mikhail B. Sevryuk

Publication date: 12 December 1993

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

Full work available at URL: https://doi.org/10.1063/1.530081

zbMATH Keywords

singular pointsturning pointsasymptotic equivalencetransformation matricesmultichannel Schrödinger equationssmall parameter at the derivativestime-dependent one- dimensional Schrödinger equations with singular potentials

Mathematics Subject Classification ID

Particular ordinary differential operators (Dirac, one-dimensional Schrödinger, etc.) (34L40) Transformation and reduction of ordinary differential equations and systems, normal forms (34C20) Perturbations of ordinary differential equations (34D10) Singular perturbations, turning point theory, WKB methods for ordinary differential equations (34E20) Singular perturbations for ordinary differential equations (34E15)

Related Items (1)

Adiabatic and post-adiabatic representations for multichannel Schrödinger equations

Cites Work

• Uniform asymptotic solutions of boundary and eigenvalue problems for a second-order ordinary differential equation with singular and turning points
• Uniform asymptotic solutions of second-order linear ordinary differential equations with singular points. I: Formal theory
• Uniform asymptotic solutions of second-order linear ordinary differential equations with singular points. II: Some expansions
• Uniform approximations for the natural modes and frequencies of spindle- shaped acoustical resonators
• Equivalence of Differential Operators
• Semiclassical Mechanics
• Langer's method for a second order linear ordinary differential equation with a double pole
• Asymptotic (short-wave) equivalence of one-dimensional Schrodinger equations by formal canonical transformations and its generalizations
• Asymptotic solution of eigenvalue problems for second-order ordinary differential equations
• Uniform Asymptotic Solutions for Linear Second Order Ordinary Differential Equations with Turning Points: Formal Theory
• Asymptotic solution of higher-order differential equations with several turning points, and application to wave propagation in slowly varying waveguides
• Uniform Asymptotic Solutions of Nonhomogeneous Differential Equations with Turning Points
• Asymptotic Solutions of Differential Equations with Transition Points or Singularities
• Uniform asymptotic solutions of second order linear ordinary differential equations with turning points
• Moments of Extinction for a Singular Perturbation Problem in the Diffusion Process

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