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Mathematics - Dynamical Systems & Differential Equations | Perturbation Theory for the Schrödinger Operator with a Periodic Potential

Perturbation Theory for the Schrödinger Operator with a Periodic Potential

Series: Lecture Notes in Mathematics, Vol. 1663

Karpeshina, Yulia E.

1997, CCCLXIV, 356 p.

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  • About this book

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.

Content Level » Research

Keywords » Potential - Schrödinger equation - operator - periodicity - perturbation theory

Related subjects » Dynamical Systems & Differential Equations - Theoretical, Mathematical & Computational Physics

Table of contents 

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.

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