On a probabilistic approach to the Schrödinger equation with a time-dependent potential

DOI10.1016/j.jfa.2010.12.007zbMath1209.35160OpenAlexW2090960083MaRDI QIDQ630789

Halim Doss

Publication date: 21 March 2011

Published in: Journal of Functional Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jfa.2010.12.007

zbMATH Keywords

Brownian motionstochastic differential equationsSchrödinger equationanalytic functionstime-dependent potentials

Mathematics Subject Classification ID

Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics (81Q05) Applications of stochastic analysis (to PDEs, etc.) (60H30) Stochastic partial differential equations (aspects of stochastic analysis) (60H15) PDEs with randomness, stochastic partial differential equations (35R60) Time-dependent Schrödinger equations and Dirac equations (35Q41)

Related Items (3)

Second-Order Hamilton–Jacobi PDE Problems and Certain Related First-Order Problems, Part 1: Approximation ⋮ A stochastic control verification theorem for the dequantized Schrödinger equation not requiring a duration restriction ⋮ Subordination principle and Feynman-Kac formulae for generalized time-fractional evolution equations

Cites Work

• The time-dependent quartic oscillator --- a Feynman path integral approach
• Sur une résolution stochastique de l'équation de Schrödinger à coefficients analytiques
• On the Schrödinger equation with potentials which are Laplace transforms of measures
• Solutions of Schrödinger equations on compact Lie groups via probabilistic methods
• Mathematical theory of Feynman path integrals. An introduction
• The Doss trick on symmetric spaces
• Feynman integrals as Hida distributions: the case of non-perturbative potentials
• Feynman integrals for a class of exponentially growing potentials
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