Perturbation Theory for the Schrödinger Operator with a Periodic Potential

• Main Author: Karpeshina, Yulia E. (Author, http://id.loc.gov/vocabulary/relators/aut)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 1997.
• Edition: 1st ed. 1997.
• Series: Lecture Notes in Mathematics, 1663
• Subjects: Partial differential equations.; Mathematical physics.; Partial Differential Equations.; Theoretical, Mathematical and Computational Physics.
• Physical Description: CCCLXIV, 356 p. online resource.
• ISBN: 9783540691563
• ISSN: 0075-8434 ;
• DOI: 10.1007/BFb0094264

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.