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024 7 $a10.1007/BFb0078115
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035   $a(DE-He213)978-3-540-45913-2
035   $a(MiAaPQ)EBC5577518
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035   $a(OCoLC)1066193714
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100   $a20220818d1988      uy             0
101 0 $aeng
135   $aurnn|008mamaa
181   $ctxt
182   $cc
183   $acr
200 10$aSemi-classical analysis for the Schro?dinger operator and applications /$fBernard Helffer
205   $a1st ed. 1988.
210  1$aBerlin :$cSpringer-Verlag,$d[1988]
210  4$d©1988
215   $a1 online resource (V, 110 p.) 
225 1 $aLecture notes in mathematics (Springer-Verlag) ;$v1336
300   $aBibliographic Level Mode of Issuance: Monograph
311   $a0-387-50076-6 
311   $a3-540-50076-6 
327   $aGeneralities 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.
330   $aThis introduction to semi-classical analysis is an extension of a course given by the author at the University of Nankai. It presents for some of the standard cases presented in quantum mechanics books a rigorous study of the tunneling effect, as an introduction to recent research work. The book may be read by a graduate student familiar with the classic book of Reed-Simon, and for some chapters basic notions in differential geometry. The mathematician will find here a nice application of PDE techniques and the physicist will discover the precise link between approximate solutions (B.K.W. constructions) and exact eigenfunctions (in every dimension). An application to Witten's approach for the proof of the Morse inequalities is given, as are recent results for the Schrödinger operator with periodic potentials.
410  0$aLecture notes in mathematics (Springer-Verlag) ;$v1336.
606   $aSchro?dinger operator
606   $aDifferential equations, Partial$xAsymptotic theory
606   $aSpectral theory (Mathematics)
615  0$aSchro?dinger operator.
615  0$aDifferential equations, Partial$xAsymptotic theory.
615  0$aSpectral theory (Mathematics)
676   $a515.724
700   $aHelffer$b Bernard$052445
801  0$bMiAaPQ
801  1$bMiAaPQ
801  2$bMiAaPQ
906   $aBOOK
912   $a996466478203316
996   $aSemi-classical analysis for the Schrodinger operator and applications$9262250
997   $aUNISA