Phase integral approximation for coupled ordinary differential equations of the Schrödinger type

DOI10.1063/1.2919888zbMath1152.81607arXiv0710.5868OpenAlexW2017396972MaRDI QIDQ5504934

Andrzej A. Skorupski

Publication date: 23 January 2009

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

Full work available at URL: https://arxiv.org/abs/0710.5868

Mathematics Subject Classification ID

Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics (81Q05) Schrödinger operator, Schrödinger equation (35J10) Semiclassical techniques, including WKB and Maslov methods applied to problems in quantum theory (81Q20)

Related Items (1)

Instability of the finite-difference split-step method applied to the nonlinear Schrödinger equation. I. standing soliton

Uses Software

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Cites Work

• Improved higher order phase-integral approximations of the JWKB type in the vicinity of zeros and singularities of the wave number
• A direct method for modifying certain phase-integral approximations of arbitrary order
• Computation of a class of functions useful in the phase-integral approximation. I: Results
• Wave propagation in complex systems of cutoffs and resonances
• Physical Problems Solved by the Phase-Integral Method
• Extension of the WKB Equation
• Detailed behavior of the phase-integral approximations at zeros and singularities of the square of the base function
• Efficient integration of the one-dimensional time independent wave equation for bound states and for wave propagation
• Adiabatic expansions of solutions of coupled second-order linear differential equations. II
• Eigenvalue problem for a set of coupled Schrödinger like ODEs
• A WKB-Type Approximation to the Schrödinger Equation

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