000 04176nam a22005415i 4500
001 978-0-8176-4662-2
003 DE-He213
005 20140220083227.0
007 cr nn 008mamaa
008 120427s2012 xxu| s |||| 0|eng d
020 _a9780817646622
_9978-0-8176-4662-2
024 7 _a10.1007/978-0-8176-4662-2
_2doi
050 4 _aQA401-425
050 4 _aQC19.2-20.85
072 7 _aPHU
_2bicssc
072 7 _aSCI040000
_2bisacsh
082 0 4 _a530.15
_223
100 1 _aGitman, D.M.
_eauthor.
245 1 0 _aSelf-adjoint Extensions in Quantum Mechanics
_h[electronic resource] :
_bGeneral Theory and Applications to Schrödinger and Dirac Equations with Singular Potentials /
_cby D.M. Gitman, I.V. Tyutin, B.L. Voronov.
264 1 _aBoston :
_bBirkhäuser Boston,
_c2012.
300 _aXIII, 511p. 3 illus.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aProgress in Mathematical Physics ;
_v62
505 0 _aIntroduction -- 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.
520 _aQuantization 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.
650 0 _aMathematics.
650 0 _aOperator theory.
650 0 _aQuantum theory.
650 0 _aMathematical physics.
650 1 4 _aMathematics.
650 2 4 _aMathematical Physics.
650 2 4 _aMathematical Methods in Physics.
650 2 4 _aOperator Theory.
650 2 4 _aQuantum Physics.
650 2 4 _aApplications of Mathematics.
700 1 _aTyutin, I.V.
_eauthor.
700 1 _aVoronov, B.L.
_eauthor.
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9780817644000
830 0 _aProgress in Mathematical Physics ;
_v62
856 4 0 _uhttp://dx.doi.org/10.1007/978-0-8176-4662-2
912 _aZDB-2-SMA
999 _c100213
_d100213