Semi-classical analysis for the Schrödinger operator and applications
By: Bernard Helffer.
Series: Lecture notes in mathematics ;; 1336; Lecture notes in mathematics (Springer-Verlag) ;; 1336.
Publisher: Springer-Verlag
Published: 1988
Place of publication: Berlin; New York
Language: eng
Number of pages: 107
Subjects: Schrödinger operator.; Differential equations, Partial -- Asymptotic theory.; Spectral theory (Mathematics)
Description: 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.
Notes: Includes bibliographical references (p. [100]-105) and index.
"Nankai Institute of Mathematics, (Tianjin, P.R. China),vol. 4."