D. M. Gitman, I. V. Tyutin, B. L. Voronov

Self-adjoint Extensions in Quantum Mechanics (eBook, PDF)

General Theory and Applications to Schrödinger and Dirac Equations with Singular Potentials

• Format: PDF

Produktbeschreibung

This exposition is devoted to a consistent treatment of quantization problems, based on appealing to some nontrivial items of functional analysis concerning the theory of linear operators in Hilbert spaces. It begins by considering quantization problems in general, emphasizing the non-triviality of consistent operator construction by presenting paradoxes to the naive treatment. It then builds the necessary mathematical background following it by the theory of self-adjoint extensions. By considering several problems such as the one-dimensional Calogero problem, the Aharonov-Bohm problem, the problem of delta-like potentials and relativistic Coulomb problemIt then shows how quantization problems associated with correct definition of observables can be treated consistently for comparatively simple quantum-mechanical systems. In the end, related problems in quantum field theory are briefly introduced. This well organized text is most suitable for students and post graduates interested in deepening their understanding of mathematical problems in quantum mechanics. However, scientists in mathematical and theoretical physics and mathematicians will also find it useful.

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Produktdetails

• Verlag: Birkhäuser Boston
• Seitenzahl: 511
• Erscheinungstermin: 27. April 2012
• Englisch
• ISBN-13: 9780817646622
• Artikelnr.: 37358660

Inhaltsangabe

Introduction.- Linear Operators in Hilbert Spaces.- Basics of Theory of s.a. Extensions of Symmetric Operators.- Differential Operators.- Spectral Analysis of s.a. Operators.- Free One-Dimensional Particle on an Interval.- One-Dimensional Particle in Potential Fields.- Schrödinger Operators with Exactly Solvable Potentials.- Dirac Operator with Coulomb Field.- Schrödinger and Dirac Operators with Aharonov-Bohm and Magnetic-Solenoid Fields.

Rezensionen

From the reviews:
"In an infinite-dimensional Hilbert space a symmetric, unbounded operator is not necessarily self-adjoint. ... The monograph by Gitman, Tyutin and Voronov is devoted to this problem. Its aim is to provide students and researchers in mathematical and theoretical physics with mathematical background on the theory of self-adjoint operators." (Rupert L. Frank, Mathematical Reviews, February, 2013)