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Semi-Classical Analysis for the Schrödinger Operator and Applications

Bernard Helffer (Autor)

Buch | Softcover

V, 110 Seiten

1988 | 1988
Springer Berlin (Verlag)
978-3-540-50076-6 (ISBN)

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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.

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.

Erscheint lt. Verlag	27.7.1988
Reihe/Serie	Lecture Notes in Mathematics
Reihe/Serie	Nankai Institute of Mathematics, Tianjin, P.R. China
Zusatzinfo	V, 110 p.
Verlagsort	Berlin
Sprache	englisch
Maße	155 x 235 mm
Gewicht	181 g
Themenwelt	Mathematik / Informatik ► Mathematik ► Analysis
	Naturwissenschaften ► Physik / Astronomie ► Allgemeines / Lexika
	Naturwissenschaften ► Physik / Astronomie ► Quantenphysik
	Naturwissenschaften ► Physik / Astronomie ► Theoretische Physik
Schlagworte	Calculus • differential equation • Minimum • Potential • quantum mechanics
ISBN-10	3-540-50076-6 / 3540500766
ISBN-13	978-3-540-50076-6 / 9783540500766
Zustand	Neuware