| Description |
1 online resource (xiii, 511 pages) |
| Series |
Progress in mathematical physics ; v. 62 |
|
Progress in mathematical physics ; v. 62.
|
| Contents |
Introduction -- Linear Operators in Hilbert Spaces -- Basics of the Theory of Self-adjoint Extensions of Symmetric Operators -- Differential Operators -- Spectral Analysis of Self-adjoint Operators -- Free One-Dimensional Particle on an Interval -- A One-Dimensional Particle in a Potential Field -- Schrödinger Operators with Exactly Solvable Potentials -- Dirac Operator with Coulomb Field -- Schrödinger and Dirac Operators with Aharonov-Bohm and Magnetic-Solenoid Fields |
| Summary |
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 |
| Analysis |
Mathematics |
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Operator theory |
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Quantum theory |
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Mathematical physics |
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Mathematical Methods in Physics |
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Quantum Physics |
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Applications of Mathematics |
|
fysica |
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physics |
|
toegepaste wiskunde |
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applied mathematics |
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quantumfysica |
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wiskunde |
|
mathematische natuurkunde |
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Mathematics (General) |
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Wiskunde (algemeen) |
| Bibliography |
Includes bibliographical references and index |
| Notes |
English |
| Subject |
Quantum theory -- Mathematics
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Schrödinger equation.
|
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Dirac equation.
|
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Mathematics.
|
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Physics.
|
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Quantum theory.
|
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Mathematical Concepts
|
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Mathematics
|
|
Physics
|
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Quantum Theory
|
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physics.
|
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SCIENCE -- Physics -- Quantum Theory.
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Matemáticas
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Física
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Quanta, Teoría de los -- Matemáticas
|
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Schrödinger, Ecuación de
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Quantum theory
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Physics
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Mathematics
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Dirac equation
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Quantum theory -- Mathematics
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Schrödinger equation
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| Form |
Electronic book
|
| Author |
Ti︠u︡tin, I. V. (Igorʹ Viktorovich)
|
|
Voronov, B. L. (Boris Leonidovich)
|
| ISBN |
9780817646622 |
|
0817646620 |
|
128080257X |
|
9781280802577 |
|
9786613710925 |
|
661371092X |
|
