Perturbation Theory for the Schrödinger Operator with a Periodic Potential

1. Front Matter

   Pages I-VII

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2. Introduction

   • Yulia E. Karpeshina

   Pages 1-22

3. Perturbation theory for a polyharmonic operator in the case of 2l>n

   • Yulia E. Karpeshina

   Pages 23-62

4. Perturbation theory for the polyharmonic operator in the case 4l>n+1

   • Yulia E. Karpeshina

   Pages 63-97

5. Perturbation theory for Schrödinger operator with a periodic potential

   • Yulia E. Karpeshina

   Pages 99-232

6. The interaction of a free wave with a semi-bounded crystal

   • Yulia E. Karpeshina

   Pages 233-338

7. Back Matter

   Pages 339-352

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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.

• Potential
• Schrödinger equation
• operator
• periodicity
• perturbation theory
• partial differential equations

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