Semi-Classical Analysis for the Schrödinger Operator and Applications

1988
ISBN: 978-3-540-50076-6
Verlag: Springer Berlin Heidelberg

Buch, Englisch, 110 Seiten, Format (B × H): 155 mm x 235 mm, Gewicht: 195 g

Reihe: Nankai Institute of Mathematics, Tianjin, P.R. China

This introduction to semi-classical analysis is an extension of a course given by the author at the University of Nankai. It presents for some of the standard cases presented in quantum mechanics books a rigorous study of the tunneling effect, as an introduction to recent research work. The book may be read by a graduate student familiar with the classic book of Reed-Simon, and for some chapters basic notions in differential geometry. The mathematician will find here a nice application of PDE techniques and the physicist will discover the precise link between approximate solutions (B.K.W. constructions) and exact eigenfunctions (in every dimension). An application to Witten's approach for the proof of the Morse inequalities is given, as are recent results for the Schrödinger operator with periodic potentials.

Zielgruppe

Research

Autoren/Hrsg.

Helffer, Bernard

Fachgebiete

• Mathematik | Informatik Mathematik Mathematische Analysis
• Naturwissenschaften Physik Quantenphysik
• Naturwissenschaften Physik Physik Allgemein Theoretische Physik, Mathematische Physik, Computerphysik

Inhaltsverzeichnis

Generalities on semi-classical analysis.- B.K.W. Construction for a potential near the bottom in the case of non-degenerate minima.- The decay of the eigenfunctions.- Study of interaction between the wells.- An introduction to recent results of Witten.- On Schrödinger operators with periodic electric potentials.- On Schrödinger operators with magnetic fields.