Perturbation Theory for the Schrödinger Operator with a Periodic Potential
Karpeshina, Yulia E.
Perturbation Theory for the Schrödinger Operator with a Periodic Potential [electronic resource] / by Yulia E. Karpeshina. - CCCLXIV, 356 p. online resource. - Lecture Notes in Mathematics, 1663 0075-8434 ; . - Lecture Notes in Mathematics, 1663 .
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.
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.
9783540691563
10.1007/BFb0094264 doi
Differential equations, partial.
Partial Differential Equations.
Theoretical, Mathematical and Computational Physics.
QA370-380
515.353
Perturbation Theory for the Schrödinger Operator with a Periodic Potential [electronic resource] / by Yulia E. Karpeshina. - CCCLXIV, 356 p. online resource. - Lecture Notes in Mathematics, 1663 0075-8434 ; . - Lecture Notes in Mathematics, 1663 .
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.
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.
9783540691563
10.1007/BFb0094264 doi
Differential equations, partial.
Partial Differential Equations.
Theoretical, Mathematical and Computational Physics.
QA370-380
515.353