Perturbation Theory for the Schrödinger Operator with a Periodic Potential

von Yulia E. Karpeshina

356 Seiten, Taschenbuch

Kurzbeschreibung des Verlags

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.

• Reihe: Lecture Notes in Mathematics
• ISBN: 9783540631361
• Sprache: Englisch
• Erscheinungsdatum: 19.08.1997
• Genre: Mathematik/Analysis
• Verlag: Springer Berlin