Stationary phase method in infinite dimensions by finite dimensional approximations: Applications to the Schrödinger equation
From MaRDI portal
Publication:1904126
DOI10.1007/BF01048065zbMath0845.58019MaRDI QIDQ1904126
Zdzisław Brzeźniak, Sergio A. Albeverio, Anne Boutet de Monvel-Berthier
Publication date: 1 February 1996
Published in: Potential Analysis (Search for Journal in Brave)
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)
Related Items (5)
Probability and Quantum Symmetries. II. The Theorem of Nœther in quantum mechanics ⋮ Uniform asymptotic bounds for the heat kernel and the trace of a stochastic geodesic flow ⋮ Mathematical theory of Feynman path integrals ⋮ Uniform convergence for complex diffusion equation via a probabilistic approach and application ⋮ Asymptotic expansions for ornstein-uhlenbeck semigroups perturbed by potentials over banach spaces
Cites Work
- Singularities of differentiable maps, Volume 2. Monodromy and asymptotics of integrals. Transl. from the Russian by Hugh Porteous and revised by the authors and James Montaldi
- Remark on the solution of the Schrödinger equation for anharmonic oscillators via the Feynman path integral
- Intégrales oscillantes stochastiques: Estimation asymptotique de fonctionnelles caractéristiques
- The method of stationary phase for oscillatory integrals on Hilbert spaces
- Analytic and sequential Feynman integrals on abstract Wiener and Hilbert spaces, and a Cameron-Martin formula
- Feynman-Kac formula associated with a system of partial differential operators
- Laplace approximations for sums of independent random vectors. II: Degenerate maxima and manifolds of maxima
- On the cylindrical approximation of the Feynman path integral
- Oscillatory integrals and the method of stationary phase in infinitely many dimensions, with applications to the classical limit of quantum mechanics. I
- Feynman path integrals and the trace formula for the Schrödinger operators
- Chaos in classical and quantum mechanics
- Semi-classical analysis for the Schrödinger operator and applications
- Mathematical theory of Feynman path integrals
- Product formulas for the eigenvalues of a class of boundary value problems
- Finite dimensional approximation approach to oscillatory integrals and stationary phase in infinite dimensions
- Time-Delay Operators in Semiclassical Limit. II. Short-Range Potentials
- A simple definition of the Feynman integral, with applications
- Conditional Analytic Feynman Integrals on Abstract Wiener Spaces
- The stationary phase method with an estimate of the remainder term on a space of large dimension
- On the convergence of the Feynman path integral for a certain class of potentials
- Asymptotic Analysis of Gaussian Integrals. I. Isolated Minimum Points
- The semi-classical expansion for a charged particle on a curved space background
- Methods de laplace et de la phase stationnaire sur l'espace de wiener
- On a double Riemann–Hilbert approach to stimulated Raman scattering
- Classical mechanics, the diffusion (heat) equation, and the Schrödinger equation
- An Introduction to Catastrophe Theory and Its Applications
- Oscillatory integrals, lagrange immersions and unfolding of singularities
- Semi-classical bounds for resolvents of schrödinger operators and asymptotics for scattering phases
- Infinite-dimensional elliptic operators and parabolic equations connected with them
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
This page was built for publication: Stationary phase method in infinite dimensions by finite dimensional approximations: Applications to the Schrödinger equation
