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Semi-Classical Analysis for the Schrödinger Operator and Applications

✍ Scribed by Bernard Helffer

Publisher
Springer
Year
1988
Tongue
English
Leaves
116
Series
Lecture Notes in Mathematics 1336
Edition
1
Category
Library
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✦ Synopsis

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 Schr?dinger operator with periodic potentials.

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