Helffer, Bernard 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 Cited in 2 ReviewsCited in 170 Documents MSC: 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 Keywords:tunneling effect; quantum mechanics; B. K. W. Constructions; decay of eigenfunctions; interaction; potential wells; periodic electric potentials; Schrödinger operators with magnetic fields × Cite Format Result Cite Review PDF