Perturbation theory for the Schrödinger operator with a periodic potential
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The book is devoted to perturbation theory for the Schrödinger 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 Schrödinger 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.
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Perturbation theory for the Schrödinger operator with a periodic potential, Julija E. Karpešina
- Language
- Released
- 1997
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- Title
- Perturbation theory for the Schrödinger operator with a periodic potential
- Language
- English
- Authors
- Julija E. Karpešina
- Publisher
- Springer
- Released
- 1997
- ISBN10
- 3540631364
- ISBN13
- 9783540631361
- Series
- Lecture notes in mathematics
- Category
- Mathematics
- Description
- The book is devoted to perturbation theory for the Schrödinger 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 Schrödinger 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.