Semi-classical analysis for the Schrödinger operator and applications. (English) Zbl 0647.35002

Lecture Notes in Mathematics, 1336. Berlin etc.: Springer-Verlag. iv, 107 p. DM 23.00 (1988).
This book is a very nice introduction to recent and deep results obtained by the author and J. Sjöstrand about the tunneling effect in quantum mechanics. Here the author gives a simpler method than in the original papers, less general but easier to understand. The content of this book concerns essentially: B. K. W. Constructions, decay of eigenfunctions, interaction between different potential wells. In the two last parts there are also results about periodic electric potentials and on Schrödinger operators with magnetic fields.
Reviewer: R.Didier


35-02 Research exposition (monographs, survey articles) pertaining to partial differential equations
35P05 General topics in linear spectral theory for PDEs
35J10 Schrödinger operator, Schrödinger equation
81Q15 Perturbation theories for operators and differential equations in quantum theory