Author	Karpeshina, Yulia E. author
Title	Perturbation Theory for the Schrรถdinger Operator with a Periodic Potential [electronic resource] / by Yulia E. Karpeshina
Imprint	Berlin, Heidelberg : Springer Berlin Heidelberg, 1997
Connect to	http://dx.doi.org/10.1007/BFb0094264
Descript	CCCLXIV, 356 p. online resource

The book is devoted to perturbation theory for the Schrรถdinger 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 Schrรถdinger 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

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 Schrรถdinger operator with a periodic potential -- The interaction of a free wave with a semi-bounded crystal

1. Mathematics
2. Partial differential equations
3. Physics
4. Mathematics
5. Partial Differential Equations
6. Theoretical
7. Mathematical and Computational Physics