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[Lecture Notes in Mathematics] Semi-Classical Analysis for the Schrödinger Operator and Applications Volume 1336 || An introduction to recent results of Witten

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Book ID
120832192
Publisher
Springer Berlin Heidelberg
Year
1988
Tongue
German
Weight
301 KB
Edition
1988
Category
Article
ISBN
3540500766

No coin nor oath required. For personal study only.

✦ Synopsis

This 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.

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[Lecture Notes in Mathematics] Semi-Classical Analysis for the Schrödinger Operator and Applications Volume 1336 || Generalities on semi-classical analysis
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This 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

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[Lecture Notes in Mathematics] Semi-Classical Analysis for the Schrödinger Operator and Applications Volume 1336 || On Schrödinger operators with periodic electric potentials
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[Lecture Notes in Mathematics] Semi-Classical Analysis for the Schrödinger Operator and Applications Volume 1336 || The decay of the eigenfunctions
✍ , 📂 Article 📅 1988 🏛 Springer Berlin Heidelberg 🌐 German ⚖ 349 KB

This 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

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[Lecture Notes in Mathematics] Semi-Classical Analysis for the Schrödinger Operator and Applications Volume 1336 || Study of interaction between the wells
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This 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

[Lecture Notes in Mathematics] Semi-Clas
[Lecture Notes in Mathematics] Semi-Classical Analysis for the Schrödinger Operator and Applications Volume 1336 || B.K.W. Construction for a potential near the bottom in the case of non-degenerate minima
✍ , 📂 Article 📅 1988 🏛 Springer Berlin Heidelberg 🌐 German ⚖ 358 KB

This 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