Time evolution kernels: uniform asymptotic expansions

DOI10.1063/1.525835zbMath0526.47029OpenAlexW2040941836MaRDI QIDQ3041825

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Publication date: 1983

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

Full work available at URL: https://doi.org/10.1063/1.525835

zbMATH Keywords

asymptotic expansionSchrödinger operatormultiplication operatoranalytic semigroup kernelconstructive series representation

Mathematics Subject Classification ID

Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics (81Q05) Heat equation (35K05) Perturbation theory of linear operators (47A55) Groups and semigroups of linear operators (47D03) General theory of partial differential operators (47F05) Schrödinger operator, Schrödinger equation (35J10) Perturbation theories for operators and differential equations in quantum theory (81Q15)

Related Items (max. 100)

An asymptotic analysis of quantum evolution with electromagnetic fields ⋮ A Borel-like estimate for the rest of the heat kernel expansion ⋮ Propagators for relativistic systems with non-Abelian interactions ⋮ A Dyson-like expansion for solutions to the quantum Liouville equation ⋮ Unnamed Item ⋮ Schrödinger spectral kernels: High order asymptotic expansions ⋮ Quantum systems with external electromagnetic fields: The large mass asymptotics ⋮ On Convergence of the Schwinger–De Witt Expansion ⋮ Time decay and spectral kernel asymptotics ⋮ Time decay and spectral kernel asymptotics ⋮ Path integrals in N=2 supersymmetric quantum mechanics

Cites Work

• A construction of the fundamental solution for the Schrödinger equation
• An asymptotic expansion for the heat equation
• Schrödinger semigroups
• Error Bounds for Asymptotic Expansions of Integrals
• The Local Geometric Asymptotics of Continuum Eigenfunction Expansions I. Overview
• Quantum Statistics of Almost Classical Assemblies
• The Asymptotic Distribution of Eigenvalues and Eigenfunctions for Elliptic Boundary Value Problems

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