Self-adjoint Extensions in Quantum Mechanics: General Theory and Applications to Schr÷dinger and Dirac Equations With Singular Potentials

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9780817644000: Self-adjoint Extensions in Quantum Mechanics: General Theory and Applications to Schr÷dinger and Dirac Equations With Singular Potentials

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. The authors begin by considering quantization problems in general, emphasizing the nontriviality 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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Recensione:

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)

Dalla quarta di copertina:

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 “naïve”  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 naïve 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.

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1.

Gitman, Dmitry; Tyutin, Igor; Voronov, Boris
ISBN 10: 0817644008 ISBN 13: 9780817644000
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Descrizione libro Condizione libro: New. Depending on your location, this item may ship from the US or UK. Codice libro della libreria 97808176440000000000

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Gitman, Dmitry; Tyutin, Igor; Voronov, Boris
ISBN 10: 0817644008 ISBN 13: 9780817644000
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Descrizione libro Condizione libro: New. This item is Print on Demand - Depending on your location, this item may ship from the US or UK. Codice libro della libreria POD_9780817644000

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Dmitry Gitman, Igor Tyutin, Boris Voronov
Editore: BIRKHAUSER BOSTON INC, United States (2012)
ISBN 10: 0817644008 ISBN 13: 9780817644000
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Descrizione libro BIRKHAUSER BOSTON INC, United States, 2012. Hardback. Condizione libro: New. 2012 ed.. 246 x 232 mm. Language: English . Brand New Book. 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. The authors begin by considering quantization problems in general, emphasizing the nontriviality 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. Codice libro della libreria LIB9780817644000

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4.

Dmitry Gitman, Igor Tyutin, Boris Voronov
Editore: BIRKHAUSER BOSTON INC, United States (2012)
ISBN 10: 0817644008 ISBN 13: 9780817644000
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Descrizione libro BIRKHAUSER BOSTON INC, United States, 2012. Hardback. Condizione libro: New. 2012 ed.. 246 x 232 mm. Language: English . Brand New Book. 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. The authors begin by considering quantization problems in general, emphasizing the nontriviality 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. Codice libro della libreria LIB9780817644000

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Dmitry Gitman, Igor Tyutin, Boris Voronov
Editore: Birkhauser Boston Inc, Secaucus
ISBN 10: 0817644008 ISBN 13: 9780817644000
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Descrizione libro Birkhauser Boston Inc, Secaucus. hardback. Condizione libro: New. Codice libro della libreria 9780817644000

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6.

D.M. Gitman, I.V. Tyutin, B.L. Voronov
Editore: Birkhńuser (2012)
ISBN 10: 0817644008 ISBN 13: 9780817644000
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Descrizione libro Birkhäuser, 2012. Hardcover. Condizione libro: New. 1st. Codice libro della libreria DADAX0817644008

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Gitman, Dmitry/ Tyutin, Igor/ Voronov, Boris
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ISBN 10: 0817644008 ISBN 13: 9780817644000
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Descrizione libro Birkhauser, 2012. Hardcover. Condizione libro: Brand New. 2012 edition. 524 pages. 9.50x6.50x1.25 inches. In Stock. Codice libro della libreria __0817644008

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Gitman, D. M.; Tyutin, I. V.; Voronov, B. L.
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Descrizione libro Birkhäuser, 2012. Condizione libro: New. Codice libro della libreria L9780817644000

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D. M. Gitman
Editore: Birkhńuser Apr 2012 (2012)
ISBN 10: 0817644008 ISBN 13: 9780817644000
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Descrizione libro Birkhäuser Apr 2012, 2012. Buch. Condizione libro: Neu. 235x155x34 mm. Neuware - 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. The authors begin by considering quantization problems in general, emphasizing the nontriviality 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. 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 naïve 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 naïve 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. 511 pp. Englisch. Codice libro della libreria 9780817644000

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Gitman, D.M.; Tyutin, I.V.; Voronov, B.L.
Editore: Birkhäuser (2012)
ISBN 10: 0817644008 ISBN 13: 9780817644000
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Descrizione libro Birkhäuser, 2012. Hardcover. Condizione libro: New. book. Codice libro della libreria 0817644008

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