Feynman formula for Schrödinger-type equations with time- and space-dependent coefficients

DOI10.1134/S1061920812030077zbMath1260.81082MaRDI QIDQ1933347

A. S. Plyashechnik

Publication date: 23 January 2013

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

Mathematics Subject Classification ID

Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics (81Q05) Path integrals in quantum mechanics (81S40) Feynman integrals and graphs; applications of algebraic topology and algebraic geometry (81Q30) Time-dependent Schrödinger equations and Dirac equations (35Q41)

Related Items (14)

Dynamics of particles with anisotropic mass depending on time and position ⋮ Quasi-Feynman formulas -- a method of obtaining the evolution operator for the Schrödinger equation ⋮ New method for constructing Chernoff functions ⋮ Feynman formulas for stochastic and quantum dynamics of particles in multidimensional domains ⋮ The Method of Chernoff Approximation ⋮ Chernoff approximation of subordinate semigroups ⋮ Solution of the Schrödinger equation with the use of the translation operator ⋮ Feynman and quasi-Feynman formulas for evolution equations ⋮ Feynman formulae and phase space Feynman path integrals for tau-quantization of some Lévy-Khintchine type Hamilton functions ⋮ Formulas that represent Cauchy problem solution for momentum and position Schrödinger equation ⋮ Solution-giving formula to Cauchy problem for multidimensional parabolic equation with variable coefficients ⋮ Chernoff approximation for semigroups generated by killed Feller processes and Feynman formulae for time-fractional Fokker-Planck-Kolmogorov equations ⋮ Explicit formula for evolution semigroup for diffusion in Hilbert space ⋮ Representation of solutions of the Cauchy problem for a one-dimensional Schrödinger equation with a smooth bounded potential by quasi-Feynman formulae

Cites Work

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• Infinite-dimensional Schrödinger equations with polynomial potentials and Feynman path integrals
• Feynman formulas for particles with position-dependent mass
• Semigroups of linear operators and applications to partial differential equations
• The probabilistic Feynman-Kac formula for an infinite-dimensional Schrödinger equation with exponential and singular potentials
• Functional integrals for the Schrödinger equation on compact Riemannian manifolds
• Note on product formulas for operator semigroups
• One-Parameter Semigroups for Linear Evolution Equations
• Hamiltonian Feynman path integrals via the Chernoff formula
• Feynman Integrals and the Schrödinger Equation
• Space-Time Approach to Non-Relativistic Quantum Mechanics
• Analytic semigroups and optimal regularity in parabolic problems

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