Spectral Asymptotics in the Semi-Classical Limit

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 relation to classical trajectories and normal forms plus slow perturbations of periodic Schrdinger operators appearing in solid state physics. The text assumes no previous specialized knowledge in quantum mechanics or microlocal analysis and only general knowledge of spectral theory in Hilbert space distributions Fourier transforms and some differential geometry.