The Trace Formula for Schrödinger Operators from Infinite Dimensional Oscillatory Integrals

DOI10.1002/mana.19961820103zbMath0866.58020OpenAlexW2095806071MaRDI QIDQ4715526

Zdzisław Brzeźniak, Sergio A. Albeverio, Anne Boutet de Monvel-Berthier

Publication date: 14 January 1997

Published in: Mathematische Nachrichten (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1002/mana.19961820103

zbMATH Keywords

periodic orbitsSchrödinger operatorstrace formulaheat semigroupSchrödinger grouppotentials

Mathematics Subject Classification ID

Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics (81Q05) Asymptotic expansions of solutions to PDEs (35C20) PDEs in connection with quantum mechanics (35Q40) Applications of manifolds of mappings to the sciences (58D30) Semiclassical techniques, including WKB and Maslov methods applied to problems in quantum theory (81Q20) Dynamical aspects of finite-dimensional Hamiltonian and Lagrangian systems (37J99) Applications of functional analysis in quantum physics (46N50) Theory of singularities and catastrophe theory (58K99) Differentiable maps on manifolds (58C25) Fourier integral operators applied to PDEs (35S30)

Related Items (6)

A rigorous mathematical construction of Feynman path integrals for the Schrödinger equation with magnetic field ⋮ Mathematical Aspects of Feynman Path Integrals, Divergences, Quantum Fields and Diagrams, and Some More General Reflections ⋮ Mathematical theory of Feynman path integrals ⋮ Generalized Fresnel integrals ⋮ Feynman path integrals for polynomially growing potentials ⋮ Feynman path integrals for the inverse quartic oscillator

Cites Work

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• Selberg's trace formula for automorphic Schrödinger operators
• Chaos in classical and quantum mechanics
• Gaussian measures in Banach spaces
• Semiclassical principal symbols and Gutzwiller's trace formula
• Feynman path integrals as infinite-dimensional oscillatory integrals: Some new developments
• Methods de laplace et de la phase stationnaire sur l'espace de wiener

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