Divergence-free WKB theory

DOI10.1016/j.aop.2004.01.005zbMath1050.81018OpenAlexW2093198389MaRDI QIDQ1827542

Tadanori Hyouguchi, Satoshi Adachi, Ryohei Seto, Masahito Ueda

Publication date: 6 August 2004

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

Full work available at URL: https://doi.org/10.1016/j.aop.2004.01.005

zbMATH Keywords

divergenceWKB methodssemiclassical quantum dynamics

Mathematics Subject Classification ID

Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics (81Q05) Nonperturbative methods of renormalization applied to problems in quantum field theory (81T16) Semiclassical techniques, including WKB and Maslov methods applied to problems in quantum theory (81Q20)

Related Items (7)

Localization phenomena in nonlinear Schrödinger equations with spatially inhomogeneous nonlinearities: theory and applications to Bose-Einstein condensates ⋮ Generalized finite moments and Liouville-Green approximations ⋮ The WKB method and differential consequences of the Riccati equation ⋮ Formal analytical solutions for the Gross-Pitaevskii equation ⋮ Hilbert’s 6th Problem: exact and approximate hydrodynamic manifolds for kinetic equations ⋮ Semiclassical anomalies of the quantum mechanical systems and their modifications for the asymptotic matching ⋮ WKB and “cubic-WKB” methods as an adiabatic approximation

Cites Work

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• The method of comparison equations in the solution of linear second-order differential equations (generalized W.K.B. method)
• Perturbation methods and non-linear hyperbolic waves
• Local Momentum in Wave Mechanics. II
• On the Connection Formulas and the Solutions of the Wave Equation
• A WKB-Type Approximation to the Schrödinger Equation

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