Rate of convergence of Feynman approximations of semigroups generated by the oscillator Hamiltonian

DOI10.1007/s11232-012-0090-xzbMath1280.81046OpenAlexW2059932106MaRDI QIDQ394851

O. G. Smolyanov, Yu. N. Orlov, V. Zh. Sakbaev

Publication date: 28 January 2014

Published in: Theoretical and Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11232-012-0090-x

zbMATH Keywords

Wigner functionharmonic oscillatorFeynman formulaChernoff theoremfinitely multiple approximationlinear quantization

Mathematics Subject Classification ID

Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics (81Q05) Phase-space methods including Wigner distributions, etc. applied to problems in quantum mechanics (81S30) Commutation relations and statistics as related to quantum mechanics (general) (81S05) Schrödinger and Feynman-Kac semigroups (47D08)

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Cites Work

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• Feynman formulas for the diffusion of particles with position-dependent mass
• Feynman formula for a class of second-order parabolic equations in a bounded domain
• Dynamics of a quantum particle with discontinuous position-dependent mass
• Feynman formulae for Feller semigroups
• Feynman formulas generated by self-adjoint extensions of the Laplacian
• Feynman formulas for particles with position-dependent mass
• Mathematical theory of Feynman path integrals. An introduction
• Note on product formulas for operator semigroups
• Hamiltonian Feynman path integrals via the Chernoff formula
• Feynman Integrals and the Schrödinger Equation
• Space-Time Approach to Non-Relativistic Quantum Mechanics
• An Operator Calculus Having Applications in Quantum Electrodynamics
• Functional Integration