國立虎尾科技大學 |

Mathematical Concepts of Quantum Mechanics

Record Type:	Language materials, printed : Monograph/item
Title/Author:	Mathematical Concepts of Quantum Mechanics/ by Stephen J. Gustafson, Israel Michael Sigal.
Author:	Gustafson, Stephen J.
other author:	Sigal, Israel Michael.
Description:	XIV, 456 p. 33 illus.online resource. :
Contained By:	Springer Nature eBook
Subject:	Functional analysis. -
Online resource:	https://doi.org/10.1007/978-3-030-59562-3
ISBN:	9783030595623

Mathematical Concepts of Quantum Mechanics
Gustafson, Stephen J.

Mathematical Concepts of Quantum Mechanics[electronic resource] /by Stephen J. Gustafson, Israel Michael Sigal. - 3rd ed. 2020. - XIV, 456 p. 33 illus.online resource. - Universitext,0172-5939. - Universitext,.

1 Physical Background -- 2 Dynamics -- 3 Observables -- 4 Quantization -- 5 Uncertainty Principle and Stability of Atoms and Molecules -- 6 Spectrum and Dynamics -- 7 Special Cases -- 8 Bound States and Variational Principle -- 9 Scattering States -- Existence of Atoms and Molecules -- 11 Perturbation Theory: Feshbach-Schur Method -- 12 Born-Oppenheimer Approximation and Adiabatic Dynamics -- 13 General Theory of Many-particle Systems -- 14 Self-consistent Approximations -- 15 The Feynman Path Integral -- 16 Semi-classical Analysis -- 17 Resonances -- 18 Quantum Statistics -- 19 Open Quantum Systems -- 20 The Second Quantization -- 21 Quantum Electro-Magnetic Field – Photons -- 22 Standard Model of Non-relativistic Matter and Radiation -- 23 Theory of Radiation -- 24 Renormalization Group -- 25 Mathematical Supplement: Spectral Analysis -- 26 Mathematical Supplement: The Calculus of Variations -- 27 Comments on Literature, and Further Reading -- References -- Index.

The book gives a streamlined introduction to quantum mechanics while describing the basic mathematical structures underpinning this discipline. Starting with an overview of key physical experiments illustrating the origin of the physical foundations, the book proceeds with a description of the basic notions of quantum mechanics and their mathematical content. It then makes its way to topics of current interest, specifically those in which mathematics plays an important role. The more advanced topics presented include: many-body systems, modern perturbation theory, path integrals, the theory of resonances, adiabatic theory, geometrical phases, Aharonov-Bohm effect, density functional theory, open systems, the theory of radiation (non-relativistic quantum electrodynamics), and the renormalization group. With different selections of chapters, the book can serve as a text for an introductory, intermediate, or advanced course in quantum mechanics. Some of the sections could be used for introductions to geometrical methods in Quantum Mechanics, to quantum information theory and to quantum electrodynamics and quantum field theory.

ISBN: 9783030595623

Standard No.: 10.1007/978-3-030-59562-3doiSubjects--Topical Terms:

527706
Functional analysis.

LC Class. No.: QA319-329.9

Dewey Class. No.: 515.7

Mathematical Concepts of Quantum Mechanics
LDR:03477nam a22003975i 4500 001 1018982
003 DE-He213
005 20201021043403.0
007 cr nn 008mamaa
008 210318s2020 gw | s |||| 0|eng d
020 $a 9783030595623 $9 978-3-030-59562-3
024 7 $a 10.1007/978-3-030-59562-3 $2 doi
035 $a 978-3-030-59562-3
050 4 $a QA319-329.9
072 7 $a PBKF $2 bicssc
072 7 $a MAT037000 $2 bisacsh
072 7 $a PBKF $2 thema
082 0 4 $a 515.7 $2 23
100 1 $a Gustafson, Stephen J. $4 aut $4 http://id.loc.gov/vocabulary/relators/aut $3 816066
245 1 0 $a Mathematical Concepts of Quantum Mechanics $h [electronic resource] / $c by Stephen J. Gustafson, Israel Michael Sigal.
250 $a 3rd ed. 2020.
264 1 $a Cham : $b Springer International Publishing : $b Imprint: Springer, $c 2020.
300 $a XIV, 456 p. 33 illus. $b online resource.
336 $a text $b txt $2 rdacontent
337 $a computer $b c $2 rdamedia
338 $a online resource $b cr $2 rdacarrier
347 $a text file $b PDF $2 rda
490 1 $a Universitext, $x 0172-5939
505 0 $a 1 Physical Background -- 2 Dynamics -- 3 Observables -- 4 Quantization -- 5 Uncertainty Principle and Stability of Atoms and Molecules -- 6 Spectrum and Dynamics -- 7 Special Cases -- 8 Bound States and Variational Principle -- 9 Scattering States -- Existence of Atoms and Molecules -- 11 Perturbation Theory: Feshbach-Schur Method -- 12 Born-Oppenheimer Approximation and Adiabatic Dynamics -- 13 General Theory of Many-particle Systems -- 14 Self-consistent Approximations -- 15 The Feynman Path Integral -- 16 Semi-classical Analysis -- 17 Resonances -- 18 Quantum Statistics -- 19 Open Quantum Systems -- 20 The Second Quantization -- 21 Quantum Electro-Magnetic Field – Photons -- 22 Standard Model of Non-relativistic Matter and Radiation -- 23 Theory of Radiation -- 24 Renormalization Group -- 25 Mathematical Supplement: Spectral Analysis -- 26 Mathematical Supplement: The Calculus of Variations -- 27 Comments on Literature, and Further Reading -- References -- Index.
520 $a The book gives a streamlined introduction to quantum mechanics while describing the basic mathematical structures underpinning this discipline. Starting with an overview of key physical experiments illustrating the origin of the physical foundations, the book proceeds with a description of the basic notions of quantum mechanics and their mathematical content. It then makes its way to topics of current interest, specifically those in which mathematics plays an important role. The more advanced topics presented include: many-body systems, modern perturbation theory, path integrals, the theory of resonances, adiabatic theory, geometrical phases, Aharonov-Bohm effect, density functional theory, open systems, the theory of radiation (non-relativistic quantum electrodynamics), and the renormalization group. With different selections of chapters, the book can serve as a text for an introductory, intermediate, or advanced course in quantum mechanics. Some of the sections could be used for introductions to geometrical methods in Quantum Mechanics, to quantum information theory and to quantum electrodynamics and quantum field theory.
650 0 $a Functional analysis. $3 527706
650 0 $a Mathematical physics. $3 527831
650 0 $a Quantum physics. $3 1179090
650 1 4 $a Functional Analysis. $3 672166
650 2 4 $a Theoretical, Mathematical and Computational Physics. $3 768900
650 2 4 $a Quantum Physics. $3 671960
700 1 $a Sigal, Israel Michael. $4 aut $4 http://id.loc.gov/vocabulary/relators/aut $3 816067
710 2 $a SpringerLink (Online service) $3 593884
773 0 $t Springer Nature eBook
776 0 8 $i Printed edition: $z 9783030595616
776 0 8 $i Printed edition: $z 9783030595630
830 0 $a Universitext, $x 0172-5939 $3 1253835
856 4 0 $u https://doi.org/10.1007/978-3-030-59562-3
912 $a ZDB-2-SMA
912 $a ZDB-2-SXMS
950 $a Mathematics and Statistics (SpringerNature-11649)
950 $a Mathematics and Statistics (R0) (SpringerNature-43713)