TY - BOOK ID - 77895942 TI - Spectral asymptotics in the semi-classical limit AU - Dimassi, Mouez AU - Sjöstrand, J PY - 1999 SN - 113988557X 1107367700 1107372240 1107362792 110736924X 1299405304 1107365244 051166219X 9781107362796 9780511662195 0521665442 9780521665445 PB - Cambridge Cambridge University Press DB - UniCat KW - Microlocal analysis. KW - Quantum theory. KW - Approximation theory. KW - Spectral theory (Mathematics) KW - Mathematical physics. KW - Physical mathematics KW - Physics KW - Functional analysis KW - Hilbert space KW - Measure theory KW - Transformations (Mathematics) KW - Theory of approximation KW - Functions KW - Polynomials KW - Chebyshev systems KW - Quantum dynamics KW - Quantum mechanics KW - Quantum physics KW - Mechanics KW - Thermodynamics KW - Mathematics UR - https://www.unicat.be/uniCat?func=search&query=sysid:77895942 AB - Semiclassical approximation addresses the important relationship between quantum and classical mechanics. There has been a very strong development in the mathematical theory, mainly thanks to methods of microlocal analysis. This book develops the basic methods, including the WKB-method, stationary phase and h-pseudodifferential operators. The applications include results on the tunnel effect, the asymptotics of eigenvalues in relation to classical trajectories and normal forms, plus slow perturbations of periodic Schrödinger operators appearing in solid state physics. No previous specialized knowledge in quantum mechanics or microlocal analysis is assumed, and only general facts about spectral theory in Hilbert space, distributions, Fourier transforms and some differential geometry belong to the prerequisites. 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. ER -