LIBERO WebOPAC Catalogue Display (W561)

Catalogue Information
Field name	Details
Dewey Class	530.15
Title	Self-adjoint Extensions in Quantum Mechanics ([EBook]) : General Theory and Applications to Schrödinger and Dirac Equations with Singular Potentials / by D.M. Gitman, I.V. Tyutin, B.L. Voronov.
Author	Gitman, Dmitrij M.
Added Personal Name	Tyutin, Igor Viktorovič
Added Personal Name	Voronov, Boris L.
Other name(s)	SpringerLink (Online service)
Publication	Boston : Birkhäuser , 2012.
Physical Details	XIII, 511 pages : 3 illus. : online resource.
Series	Progress in Mathematical Physics ; 62
ISBN	9780817646622
Summary Note	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 ânaÃ¯veâ Â 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 naÃ¯ve treatment. Â The necessary mathematical background is then built by developing the theory of self-adjoint extensions. Through examination of a 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.:
Contents note	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.
System details note	Online access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users)
Internet Site	http://dx.doi.org/10.1007/978-0-8176-4662-2
Links to Related Works	Subject References: Applications of Mathematics . Mathematical Methods in Physics . Mathematical Physics . Mathematics . Operator Theory . Quantum Physics . Quantum theory . Authors: author . Gitman, Dmitrij M. . Tyutin, Igor Viktorovič . Voronov, Boris L. . Corporate Authors: SpringerLink (Online service) . Series: Progress in Mathematical Physics . Classification: 530.15 .

Catalogue Display

Self-adjoint Extensions in Quantum Mechanics: General Theory and Applications to Schrödinger and Dirac Equations with Singular Potentials

Reviews