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Perturbation theory for the Schrödinger operator with a periodic potential / Yulia E. Karpeshina.

By: Material type: TextTextSeries: Lecture notes in mathematics (Springer-Verlag) ; 1663.Publication details: Berlin ; New York : Springer, ©1997.Description: 1 online resource (vii, 352 pages) : illustrationsContent type:
  • text
Media type:
  • computer
Carrier type:
  • online resource
ISBN:
  • 9783540691563
  • 3540691561
Subject(s): Additional physical formats: Print version:: Perturbation theory for the Schrödinger operator with a periodic potential.DDC classification:
  • 515/.7242 21
LOC classification:
  • QC174.17.S3
Other classification:
  • 31.46
Online resources:
Contents:
Introduction -- Perturbation Theory for a Polyharmonic Operator in the Case of 2l> n -- Perturbation Theory for the Polyharmonic Operator in the Case of 4l>n+1 -- Perturbation Theory for Schrdinger Operator with a Periodic Potential -- The Interaction of a Free Wave with a Semi- bounded Crystal -- References -- Index.
Summary: The book is devoted to perturbation theory for the Schrdinger operator with a periodic potential, describing motion of a particle in bulk matter. The Bloch eigenvalues of the operator are densely situated in a high energy region, so regular perturbation theory is ineffective. The mathematical difficulties have a physical nature - a complicated picture of diffraction inside the crystal. The author develops a new mathematical approach to this problem. It provides mathematical physicists with important results for this operator and a new technique that can be effective for other problems. The semiperiodic Schrdinger operator, describing a crystal with a surface, is studied. Solid-body theory specialists can find asymptotic formulae, which are necessary for calculating many physical values.
Holdings
Item type Current library Collection Call number Status Date due Barcode Item holds
eBook eBook e-Library eBook LN Mathematic Available
Total holds: 0

Includes bibliographical references (pages 339-349) and index.

Introduction -- Perturbation Theory for a Polyharmonic Operator in the Case of 2l> n -- Perturbation Theory for the Polyharmonic Operator in the Case of 4l>n+1 -- Perturbation Theory for Schrdinger Operator with a Periodic Potential -- The Interaction of a Free Wave with a Semi- bounded Crystal -- References -- Index.

The book is devoted to perturbation theory for the Schrdinger operator with a periodic potential, describing motion of a particle in bulk matter. The Bloch eigenvalues of the operator are densely situated in a high energy region, so regular perturbation theory is ineffective. The mathematical difficulties have a physical nature - a complicated picture of diffraction inside the crystal. The author develops a new mathematical approach to this problem. It provides mathematical physicists with important results for this operator and a new technique that can be effective for other problems. The semiperiodic Schrdinger operator, describing a crystal with a surface, is studied. Solid-body theory specialists can find asymptotic formulae, which are necessary for calculating many physical values.

Print version record.

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