Quantum Mechanical Path Integrals with Wiener Measures for all Polynomial Hamiltonians

DOI10.1103/PhysRevLett.52.1161zbMath0979.81518MaRDI QIDQ2770034

Ingrid Daubechies, John R. Klauder

Publication date: 14 February 2002

Published in: Physical Review Letters (Search for Journal in Brave)

Mathematics Subject Classification ID

Path integrals in quantum mechanics (81S40) Applications of manifolds of mappings to the sciences (58D30) Phase-space methods including Wigner distributions, etc. applied to problems in quantum mechanics (81S30)

Related Items (16)

Generalized Scaling Operators in White Noise Analysis and Applications to Hamiltonian Path Integrals with Quadratic Action ⋮ Landau-level ground-state degeneracy and its relevance for a general quantization procedure ⋮ Feynman path integrals on phase space and the metaplectic representation ⋮ Feynman-diagrammatic description of the asymptotics of the time evolution operator in quantum mechanics ⋮ Fermions in loop quantum gravity and resolution of doubling problem ⋮ Schrödinger dynamics in length-scale hierarchy: from spatial rescaling to Huygens-like proliferation of Gaussian wavepackets ⋮ Construction of self-adjoint Berezin-Toeplitz operators on Kähler manifolds and a probabilistic representation of the associated semigroups ⋮ Hamiltonian path integrals in momentum space representation via white noise techniques ⋮ The Hamiltonian path integral for potentials of the Albeverio Høegh-Krohn class -- a white noise approach ⋮ Feynman Integrals for a New Class of Time-Dependent Exponentially Growing Potentials ⋮ WHITE NOISE ANALYSIS: SOME APPLICATIONS IN COMPLEX SYSTEMS, BIOPHYSICS AND QUANTUM MECHANICS ⋮ Path integral of the hydrogen atom, Jacobi's principle of least action and one-dimensional quantum gravity ⋮ The Hamiltonian path integrand for the charged particle in a constant magnetic field as white noise distribution ⋮ A white noise approach to phase space Feynman path integrals ⋮ A straight forward path to a path integration of Einstein's gravity ⋮ Wiener and Poisson process regularization for coherent-state path integrals

Cites Work

• Measures for more quadratic path integrals
• The Ilstow and Feynman integrals
• Integration in Functional Spaces and its Applications in Quantum Physics
• Feynman Integrals and the Schrödinger Equation

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