Spectral Asymptotics in the Semi-Classical Limit [Paperback]

This book presents the basic methods and applications in semiclassical approximation in the light of developments.Semiclassical approximation addresses the important relationship between quantum and classical mechanics. This book presents the basic methods in the light of recent developments, including the WKB-method, stationary phase and h-pseudodifferential operators. Applications include the tunnel effect, asymptotics of eigenvalues, plus slow perturbations of periodic Schrödinger operators in solid state physics. This book is addressed to researchers and graduate students in mathematical analysis, as well as physicists who are interested in rigorous results. A fairly large fraction can be (and has been) covered in a one semester course.Semiclassical approximation addresses the important relationship between quantum and classical mechanics. This book presents the basic methods in the light of recent developments, including the WKB-method, stationary phase and h-pseudodifferential operators. Applications include the tunnel effect, asymptotics of eigenvalues, plus slow perturbations of periodic Schrödinger operators in solid state physics. This book is addressed to researchers and graduate students in mathematical analysis, as well as physicists who are interested in rigorous results. A fairly large fraction can be (and has been) covered in a one semester course.Semiclassical approximation addresses the important relationship between quantum and classical mechanics. In recent years mathematical theory has undergone significant growth, mainly due to microlocal analysis techniques. This volume develops the basic methods of the theory, including the WKB-method, stationary phase and h-pseudodifferential operators. The authors employ the systematic use of a Cauchy formula that simplifies the functional calculus of pseudodifferential operators. The applications described include recent results on the tunnel effect, the asymptotics of eigenvalues in relal“E