Perturbation Theory for the Schrödinger Operator with a Periodic Potential

ISBN-13: 9783540631361 / Angielski / Miękka / 1997 / 356 str.

Yulia E. Karpeshina

Opis

The book is devoted to perturbation theory for the Schrodinger 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 Schrodinger 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.

Spis treści

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.