Self-adjoint Extensions in Quantum Mechanics

Self-adjoint Extensions in Quantum Mechanics

Published: 2012-04-27 | ISBN: 0817644008 | PDF | 511 pages | 4 MB

Quantization of physical systems requires a correct definition of quantum-mechanical observables, such as the Hamiltonian, momentum, etc., as self-adjoint operators in appropriate Hilbert spaces and their spectral analysis. Though a "na?ve" treatment exists for dealing with such problems, it is based on finite-dimensional algebra or even infinite-dimensional algebra with bounded operators, resulting in paradoxes and inaccuracies. A proper treatment of these problems requires invoking certain nontrivial notions and theorems from functional analysis concerning the theory of unbounded self-adjoint operators and the theory of self-adjoint extensions of symmetric operators.
Self-adjoint Extensions in Quantum Mechanics begins by considering quantization problems in general, emphasizing the nontriviality of consistent operator construction by presenting paradoxes of the na?ve treatment. The necessary mathematical background is then built by developing the theory of self-adjoint extensions. Through examination of various quantum-mechanical systems, the authors show how quantization problems associated with the correct definition of observables and their spectral analysis can be treated consistently for comparatively simple quantum-mechanical systems. Systems that are examined include free particles on an interval, particles in a number of potential fields including delta-like potentials, the one-dimensional Calogero problem, the Aharonov-Bohm problem, and the relativistic Coulomb problem.
This well-organized text is most suitable for graduate students and postgraduates interested in deepening their understanding of mathematical problems in quantum mechanics beyond the scope of those treated in standard textbooks. The book may also serve as a useful resource for mathematicians and researchers in mathematical and theoretical physics.


[Fast Download] Self-adjoint Extensions in Quantum Mechanics

Ebooks related to "Self-adjoint Extensions in Quantum Mechanics" :
Electromagnetic Interactions
Lev D. Landau, Evgenij M. Lifsits, Fisica teorica VI. Meccanica dei fluidi
Advanced Methods of Continuum Mechanics for Materials and Structures
The Finite Element Analysis Program MSC Marc/Mentat: A First Introduction
Exploring Greenland: Cold War Science and Technology on Ice
Polarized Electrons at Surfaces
Magnetism: Fundamentals
Statistical Mechanics Made Simple: A Guide for Students and Researchers
Complex Space Source Theory of Spatially Localized Electromagnetic Waves
Useful Optics
Copyright Disclaimer:
This site does not store any files on its server. We only index and link to content provided by other sites. Please contact the content providers to delete copyright contents if any and email us, we'll remove relevant links or contents immediately.