Semi-classical analysis for the Schrödinger operator and applications:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Berlin [u.a.]
Springer
1988
|
| Series: | Lecture notes in mathematics
1336 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | IV, 107 S. |
| ISBN: | 3540500766 0387500766 |
Staff View
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| 245 | 1 | 0 | |a Semi-classical analysis for the Schrödinger operator and applications |c Bernard Helffer |
| 264 | 1 | |a Berlin [u.a.] |b Springer |c 1988 | |
| 300 | |a IV, 107 S. | ||
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| 490 | 1 | |a Lecture notes in mathematics |v 1336 | |
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Record in the Search Index
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| adam_text | CONTENTS
§ O Introduction lll
§ 1 Generalities on semi-classical analysis 1
§ 1.1 The classical mechanics
§ 1.2 The quantum mechanics
§ 1.3 Some basic results of the Schrodinger operator
§ 2 B.K.H Construction for a potential near the bottom in the case of non-
degenerate minima. 7
§ 2.1 The harmonic oscillator
5 2.2 Approximate solutions starting from the harmonic oscillator
§ 2.3 The B.K.W construction
§ 2.4 Proof of propositions 2.3.6 and 2.3.7
§ 3 The decay of the eigenfunctions 19
5 3.1 Energy estimates
§ 3.2 The Agmon distance
§ 3.3 Decay of eigenfunctions for the one-well Dirichlet problem
§ 3.4 Localization of the spectrum for the Dirichlet problem at the
bottom.
§ 3.5 Decay in the case of multiple wells Dirichlet problems.
§ 4 Study of interaction between the wells 3 0
§ 4.1 Preparations in functional analysis
§ 4.2 To what extent can we forget the tunneling effect
§ 4.3 The tunneling effect
§ 4.4 Study of the multiple wells problem at the bottom.
§ 4.5 The case :n=l
§ 5 An introduction to recent results of Witten 61
§ 5.1 Introduction
§ 5.2 Proof of the strong Horse inequalities
§ 6 On Schrodinger operators with periodic electric potentials 71
§ 6.1 Generalities
§ 6.2 Semi-classical study of the first eigenvalues of PJh)
§ 7 On Schrodinger operators with magnetic fields 79
§ 7.0 Introduction
§ 7.1 A criterion of compact resolvent
§ 7.2 Spectral effects due to the flux of the magnetic fields
7.2.1 A qualitative result
7.2.2 The semi-classical approach
§ 7.3 On the multiplicity of the first eigenvalue
References. 100
Index 106
|
| any_adam_object | 1 |
| author | Helffer, Bernard 1949- |
| author_GND | (DE-588)1031664645 |
| author_facet | Helffer, Bernard 1949- |
| author_role | aut |
| author_sort | Helffer, Bernard 1949- |
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| building | Verbundindex |
| bvnumber | BV000860686 |
| classification_rvk | SI 850 |
| classification_tum | PHY 013f MAT 472f |
| ctrlnum | (OCoLC)230937493 (DE-599)BVBBV000860686 |
| discipline | Physik Mathematik |
| format | Book |
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| id | DE-604.BV000860686 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T15:20:39Z |
| institution | BVB |
| isbn | 3540500766 0387500766 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-000540393 |
| oclc_num | 230937493 |
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| physical | IV, 107 S. |
| publishDate | 1988 |
| publishDateSearch | 1988 |
| publishDateSort | 1988 |
| publisher | Springer |
| record_format | marc |
| series | Lecture notes in mathematics |
| series2 | Lecture notes in mathematics Lecture notes in mathematics / Subseries: Nankai Institute of Mathematics, Tianjin, P.R. China |
| spelling | Helffer, Bernard 1949- Verfasser (DE-588)1031664645 aut Semi-classical analysis for the Schrödinger operator and applications Bernard Helffer Berlin [u.a.] Springer 1988 IV, 107 S. txt rdacontent n rdamedia nc rdacarrier Lecture notes in mathematics 1336 Lecture notes in mathematics / Subseries: Nankai Institute of Mathematics, Tianjin, P.R. China 4 Hamilton-Operator (DE-588)4072278-8 gnd rswk-swf Quasiklassisches Modell (DE-588)4318601-4 gnd rswk-swf Hamilton-Operator (DE-588)4072278-8 s Quasiklassisches Modell (DE-588)4318601-4 s DE-604 Subseries: Nankai Institute of Mathematics, Tianjin, P.R. China Lecture notes in mathematics 4 (DE-604)BV001897825 4 Lecture notes in mathematics 1336 (DE-604)BV000676446 1336 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=000540393&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Helffer, Bernard 1949- Semi-classical analysis for the Schrödinger operator and applications Lecture notes in mathematics Hamilton-Operator (DE-588)4072278-8 gnd Quasiklassisches Modell (DE-588)4318601-4 gnd |
| subject_GND | (DE-588)4072278-8 (DE-588)4318601-4 |
| title | Semi-classical analysis for the Schrödinger operator and applications |
| title_auth | Semi-classical analysis for the Schrödinger operator and applications |
| title_exact_search | Semi-classical analysis for the Schrödinger operator and applications |
| title_full | Semi-classical analysis for the Schrödinger operator and applications Bernard Helffer |
| title_fullStr | Semi-classical analysis for the Schrödinger operator and applications Bernard Helffer |
| title_full_unstemmed | Semi-classical analysis for the Schrödinger operator and applications Bernard Helffer |
| title_short | Semi-classical analysis for the Schrödinger operator and applications |
| title_sort | semi classical analysis for the schrodinger operator and applications |
| topic | Hamilton-Operator (DE-588)4072278-8 gnd Quasiklassisches Modell (DE-588)4318601-4 gnd |
| topic_facet | Hamilton-Operator Quasiklassisches Modell |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=000540393&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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