Perturbation Theory for the Schrödinger Operator with a Periodic Potential
Perturbation Theory for the Schrödinger Operator with a Periodic Potential

Author: Yulia E. Karpeshina

Publisher: Springer

Published: 2006-11-14

Total Pages: 358

ISBN-13: 3540691561

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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.

Hilbert Space Operators in Quantum Physics
Hilbert Space Operators in Quantum Physics

Author: Jirí Blank

Publisher: Springer Science & Business Media

Published: 2008-09-24

Total Pages: 677

ISBN-13: 1402088701

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The new edition of this book detailing the theory of linear-Hilbert space operators and their use in quantum physics contains two new chapters devoted to properties of quantum waveguides and quantum graphs. The bibliography contains 130 new items.

Singular Quadratic Forms in Perturbation Theory
Singular Quadratic Forms in Perturbation Theory

Author: Volodymyr Koshmanenko

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 316

ISBN-13: 9401146195

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The notion of singular quadratic form appears in mathematical physics as a tool for the investigation of formal expressions corresponding to perturbations devoid of operator sense. Numerous physical models are based on the use of Hamiltonians containing perturba tion terms with singular properties. Typical examples of such expressions are Schrodin ger operators with O-potentials (-~ + AD) and Hamiltonians in quantum field theory with perturbations given in terms of operators of creation and annihilation (P(

Mathematical Modeling in Optical Science
Mathematical Modeling in Optical Science

Author: Gang Bao

Publisher: SIAM

Published: 2001-01-01

Total Pages: 344

ISBN-13: 0898714753

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This volume addresses recent developments in mathematical modeling in three areas of optical science: diffractive optics, photonic band gap structures, and waveguides. Particular emphasis is on the formulation of mathematical models and the design and analysis of new computational approaches. The book contains cutting-edge discourses on emerging technology in optics that provides significant challenges and opportunities for applied mathematicians, researchers, and engineers. Each of the three topics is presented through a series of survey papers to provide a broad overview focusing on the mathematical models. Chapters present model problems, physical principles, mathematical and computational approaches, and engineering applications corresponding to each of the three areas. Although some of the subject matter is classical, the topics presented are new and represent the latest developments in their respective fields.