LEADER 03851nam 2200577 450 001 996418189203316 005 20220321134711.0 010 $a3-030-59562-5 024 7 $a10.1007/978-3-030-59562-3 035 $a(CKB)4100000011515583 035 $a(DE-He213)978-3-030-59562-3 035 $a(MiAaPQ)EBC6380789 035 $a(MiAaPQ)EBC6647508 035 $a(Au-PeEL)EBL6380789 035 $a(OCoLC)1204139454 035 $a(Au-PeEL)EBL6647508 035 $a(PPN)258059524 035 $a(EXLCZ)994100000011515583 100 $a20220321d2020 uy 0 101 0 $aeng 135 $aurnn|008mamaa 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aMathematical concepts of quantum mechanics /$fStephen J. Gustafson and Israel Michael Sigal 205 $aThird edition. 210 1$aCham, Switzerland :$cSpringer,$d[2020] 210 4$dİ2020 215 $a1 online resource (XIV, 456 p. 33 illus.) 225 1 $aUniversitext,$x0172-5939 311 $a3-030-59561-7 320 $aIncludes bibliographical references and index. 327 $a1 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. 330 $aThe book gives a streamlined introduction to quantum mechanics while describing the basic mathematical structures underpinning this discipline. Starting with an overview of key physical experiments illustrating the origin of the physical foundations, the book proceeds with a description of the basic notions of quantum mechanics and their mathematical content. It then makes its way to topics of current interest, specifically those in which mathematics plays an important role. The more advanced topics presented include: many-body systems, modern perturbation theory, path integrals, the theory of resonances, adiabatic theory, geometrical phases, Aharonov-Bohm effect, density functional theory, open systems, the theory of radiation (non-relativistic quantum electrodynamics), and the renormalization group. With different selections of chapters, the book can serve as a text for an introductory, intermediate, or advanced course in quantum mechanics. Some of the sections could be used for introductions to geometrical methods in Quantum Mechanics, to quantum information theory and to quantum electrodynamics and quantum field theory. 410 0$aUniversitext,$x0172-5939 606 $aQuantum theory 606 $aQuantum theory$xMathematics 606 $aMathematical physics 615 0$aQuantum theory. 615 0$aQuantum theory$xMathematics. 615 0$aMathematical physics. 676 $a530.12 700 $aGustafson$b Stephen J.$f1972-$01217095 702 $aSigal$b Israel Michael$f1945- 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a996418189203316 996 $aMathematical concepts of quantum mechanics$92814517 997 $aUNISA