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Stationary phase method in infinite dimensions by finite dimensional approximations: Applications to the Schrödinger equation. (English) Zbl 0845.58019

The authors continue their work on developing an approach by finite dimensional approximations for the study of infinite-dimensional oscillatory integrals and the relative method of stationary phase. Here the previous results are extended in several directions. In particular, the asymptotic expansions in both non-degenerate and degenerate cases are described in details. As an application a detailed asymptotic expansion in Planck’s constant for the Schrödinger equation is derived.

MSC:

58D30 Applications of manifolds of mappings to the sciences
35Q40 PDEs in connection with quantum mechanics
37J99 Dynamical aspects of finite-dimensional Hamiltonian and Lagrangian systems
81Q20 Semiclassical techniques, including WKB and Maslov methods applied to problems in quantum theory
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