000			03206nam a22004098i 4500
001			CR9780511662195
003			UkCbUP
005			20200124160241.0
006			m|||||o||d||||||||
007			cr||||||||||||
008			091215s1999||||enk o ||1 0|eng|d
020			_a9780511662195 (ebook)
020			_z9780521665445 (paperback)
040			_aUkCbUP _beng _erda _cUkCbUP
050	0	0	_aQC20.7.M53 _bD56 1999
082	0	0	_a530.15/57222 _221
100	1		_aDimassi, Mouez, _eauthor.
245	1	0	_aSpectral asymptotics in the semi-classical limit / _cMouez Dimassi, Johannes Sjöstrand.
264		1	_aCambridge : _bCambridge University Press, _c1999.
300			_a1 online resource (xi, 227 pages) : _bdigital, PDF file(s).
336			_atext _btxt _2rdacontent
337			_acomputer _bc _2rdamedia
338			_aonline resource _bcr _2rdacarrier
490	1		_aLondon Mathematical Society lecture note series ; _v268
500			_aTitle from publisher's bibliographic system (viewed on 05 Oct 2015).
505	0	0	_tLocal symplectic geometry -- _tThe WKB-method -- _tThe WKB-method for a potential minimum -- _tSelf-adjoint operators -- _tThe method of stationary phase -- _tTunnel effect and interaction matrix -- _t@h-pseudodifferential operators -- _tFunctional calculus for pseudodifferential operators -- _tTrace class operators and applications of the functional calculus -- _tMore precise spectral asymptotics for non-critical Hamiltonians -- _tImprovement when the periodic trajectories form a set of measure 0 -- _tA more general study of the trace -- _tSpectral theory for perturbed periodic problems -- _tNormal forms for some scalar pseudodifferential operators -- _tSpectrum of operators with periodic bicharacteristics.
520			_aSemiclassical 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.
650		0	_aMicrolocal analysis.
650		0	_aQuantum theory.
650		0	_aApproximation theory.
650		0	_aSpectral theory (Mathematics)
650		0	_aMathematical physics.
700	1		_aSjöstrand, J. _q(Johannes), _eauthor.
776	0	8	_iPrint version: _z9780521665445
830		0	_aLondon Mathematical Society lecture note series ; _v268.
856	4	0	_uhttps://doi.org/10.1017/CBO9780511662195
999			_c518561 _d518559