Semi-Classical Analysis for the Schrödinger Operator and Applications

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.

List of contents

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.

Product details

• Authors: Bernard Helffer
• Publisher: Springer, Berlin
• Languages: English
• Product format: Paperback / Softback
• Released: 26.06.2009
• EAN: 9783540500766
• ISBN: 978-3-540-50076-6
• No. of pages: 110
• Dimensions: 158 mm x 234 mm x 7 mm
• Weight: 214 g
• Illustrations: V, 110 p.
• Series: Lecture Notes in Mathematics / Nankai Institute of Mathematics, Tianjin, P.R. China; Lecture Notes in Mathematics; Lecture Notes in Mathematics / Nankai Institute of Mathematics, Tianjin, P.R. China; Nankai Institute of Mathematics, Tianjin, P.R. China
• Subject: Natural sciences, medicine, IT, technology > Physics, astronomy > Theoretical physics