Perturbation Theory for the Schrödinger Operator with a Periodic Potential
Perturbation Theory for the Schrödinger Operator with a Periodic Potential By Yulia E. Karpeshina (auth.)
1997 | 356 Pages | ISBN: 3540631364 | DJVU | 3 MB
1997 | 356 Pages | ISBN: 3540631364 | DJVU | 3 MB
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.