Perturbation Theory for the Schrödinger Operator with a Periodic Potential

1997
ISBN: 978-3-540-63136-1
Verlag: Springer Berlin Heidelberg

Buch, Englisch, Band 1663, 356 Seiten, Format (B × H): 155 mm x 235 mm, Gewicht: 1130 g

Reihe: Lecture Notes in Mathematics

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.

Zielgruppe

Research

Autoren/Hrsg.

Karpeshina, Yulia E.

Fachgebiete

• Mathematik | Informatik Mathematik Mathematische Analysis Funktionalanalysis
• Mathematik | Informatik Mathematik Mathematische Analysis Differentialrechnungen und -gleichungen
• Mathematik | Informatik Mathematik Mathematische Analysis Variationsrechnung
• Naturwissenschaften Biowissenschaften Angewandte Biologie Biomathematik
• Mathematik | Informatik Mathematik Mathematische Analysis Harmonische Analysis, Fourier-Mathematik
• Technische Wissenschaften Technik Allgemein Mathematik für Ingenieure

Inhaltsverzeichnis

Perturbation theory for a polyharmonic operator in the case of 2l>n.- Perturbation theory for the polyharmonic operator in the case 4l>n+1.- Perturbation theory for Schrödinger operator with a periodic potential.- The interaction of a free wave with a semi-bounded crystal.