ON THE BEHAVIOR AT INFINITY OF THE FUNDAMENTAL SOLUTION OF TIME DEPENDENT SCHRÖDINGER EQUATION

DOI10.1142/S0129055X01000910zbMath1030.35003OpenAlexW1987327794MaRDI QIDQ4418301

Kenji Yajima

Publication date: 7 August 2003

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

Full work available at URL: https://doi.org/10.1142/s0129055x01000910

zbMATH Keywords

asymptotic behaviorCauchy problemSchrödinger operator

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) Fundamental solutions to PDEs (35A08) Schrödinger operator, Schrödinger equation (35J10) Semiclassical techniques, including WKB and Maslov methods applied to problems in quantum theory (81Q20)

Related Items

GEOMETRIC APPROACH TO THE HAMILTON–JACOBI EQUATION AND GLOBAL PARAMETRICES FOR THE SCHRÖDINGER PROPAGATOR ⋮ Strichartz estimates for Schrödinger equations with variable coefficients and potentials at most linear at spatial infinity ⋮ SPATIAL GROWTH OF FUNDAMENTAL SOLUTIONS FOR CERTAIN PERTURBATIONS OF THE HARMONIC OSCILLATOR ⋮ Global parametrices for the Schrödinger propagator and geometric approach to the Hamilton-Jacobi equation ⋮ Propagation of Singularities for Schrödinger Equations on the Euclidean Space with a Scattering Metric

Cites Work

• Smoothness and non-smoothness of the fundamental solution of time dependent Schrödinger equations
• Reconstruction of singularities for solutions of Schrödinger's equation
• Remarks on convergence of the Feynman path integrals
• Boundedness and continuity of the fundamental solution of the time dependent Schrödinger equation with singular potentials
• On the fundamental solution of a perturbed harmonic oscillator
• Schrödinger semigroups
• A Symbol Class for Some Schrodinger Equations on R n
• Parametrices for a class of schrodinger equations

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