The time-dependent quartic oscillator --- a Feynman path integral approach

DOI10.1016/j.jfa.2006.01.002zbMath1130.81032OpenAlexW2057661497WikidataQ62049362 ScholiaQ62049362MaRDI QIDQ852588

Sergio A. Albeverio, Sonia Mazzucchi

Publication date: 15 November 2006

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

Full work available at URL: https://doi.org/10.1016/j.jfa.2006.01.002

zbMATH Keywords

Schrödinger equationFeynman path integralstime-dependent potentials

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) PDEs in connection with quantum mechanics (35Q40) Schrödinger operator, Schrödinger equation (35J10) Set functions and measures and integrals in infinite-dimensional spaces (Wiener measure, Gaussian measure, etc.) (28C20) Measure (Gaussian, cylindrical, etc.) and integrals (Feynman, path, Fresnel, etc.) on manifolds (46T12)

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Cites Work

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• Feynman path integrals as analysis on path space by time slicing approximation
• Some new developments in the theory of path integrals, with applications to quantum theory
• Analytic and sequential Feynman integrals on abstract Wiener and Hilbert spaces, and a Cameron-Martin formula
• Oscillatory integrals and the method of stationary phase in infinitely many dimensions, with applications to the classical limit of quantum mechanics. I
• Remarks on convergence of the Feynman path integrals
• Mathematical theory of Feynman path integrals
• On the Schrödinger equation with potentials which are Laplace transforms of measures
• Quantum mechanical propagators in terms of Hida distributions
• A representation of the Belavkin equation via Feynman path integrals
• Generalized infinite-dimensional Fresnel integrals.
• Feynman path integrals for polynomially growing potentials
• Time-dependent linear Hamiltonian systems and quantum mechanics
• Finite dimensional approximation approach to oscillatory integrals and stationary phase in infinite dimensions
• Generalized Fresnel integrals
• Smooth functional derivatives in Feynman path integrals by time slicing approximation
• Fourier integral operators. I
• Integration of the equation of evolution in a Banach space
• A Family of Integrals Serving to Connect the Wiener and Feynman Integrals
• Conditional Analytic Feynman Integrals on Abstract Wiener Spaces
• The Feynman integrand as a Hida distribution
• Feynman integrals and Fredholm determinants
• The Feynman integral for time-dependent anharmonic oscillators
• A REPRESENTATION OF THE BELAVKIN EQUATION VIA PHASE SPACE FEYNMAN PATH INTEGRALS
• Feynman integrals for a class of exponentially growing potentials
• Feynman Integrals and the Schrödinger Equation
• Space-Time Approach to Non-Relativistic Quantum Mechanics