On the cylindrical approximation of the Feynman path integral

DOI10.1016/0034-4877(78)90055-1zbMath0421.28014OpenAlexW2031402545MaRDI QIDQ1132983

S. H. Smith

Publication date: 1978

Published in: Reports on Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0034-4877(78)90055-1

zbMATH Keywords

harmonic oscillatorinteraction potentialTrotter-Kato formulaRiemannian approximationFeynman path integralcylindrical approximationglobal solution of the Schrödinger equationinitial value of the wave function

Mathematics Subject Classification ID

Path integrals in quantum mechanics (81S40) Set functions and measures and integrals in infinite-dimensional spaces (Wiener measure, Gaussian measure, etc.) (28C20)

Related Items

Stationary phase method in infinite dimensions by finite dimensional approximations: Applications to the Schrödinger equation, Oscillatory integrals and the method of stationary phase in infinitely many dimensions, with applications to the classical limit of quantum mechanics. I, Uniform product formulae with application to the Feynman-Nelson integral for open systems, Polygonal-path approximations on the path spaces of quantum-mechanical systems, Complex-potential description of the damped harmonic oscillator, Remark on the solution of the Schrödinger equation for anharmonic oscillators via the Feynman path integral, Spectral methods for nonlinear functionals and functional differential equations

Cites Work

• The semiclassical expansion
• Mathematical theory of Feynman path integrals
• Generating functions for the affine symplectic group
• A Family of Integrals Serving to Connect the Wiener and Feynman Integrals
• Feynman Integrals and the Schrödinger Equation
• Space-Time Approach to Non-Relativistic Quantum Mechanics
• Markoff chains, Wiener integrals, and quantum theory
• Produits tensoriels topologiques et espaces nucléaires
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