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020 _a9781461471165
_9978-1-4614-7116-5
024 7 _a10.1007/978-1-4614-7116-5
_2doi
050 4 _aQA401-425
050 4 _aQC19.2-20.85
072 7 _aPHU
_2bicssc
072 7 _aSCI040000
_2bisacsh
072 7 _aPHU
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082 0 4 _a530.15
_223
100 1 _aHall, Brian C.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
245 1 0 _aQuantum Theory for Mathematicians
_h[electronic resource] /
_cby Brian C. Hall.
250 _a1st ed. 2013.
264 1 _aNew York, NY :
_bSpringer New York :
_bImprint: Springer,
_c2013.
300 _aXVI, 554 p. 30 illus., 2 illus. in color.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
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_2rda
490 1 _aGraduate Texts in Mathematics,
_x0072-5285 ;
_v267
505 0 _a1 The Experimental Origins of Quantum Mechanics -- 2 A First Approach to Classical Mechanics -- 3 A First Approach to Quantum Mechanics -- 4 The Free Schrödinger Equation -- 5 A Particle in a Square Well -- 6 Perspectives on the Spectral Theorem -- 7 The Spectral Theorem for Bounded Self-Adjoint Operators: Statements -- 8 The Spectral Theorem for Bounded Sef-Adjoint Operators: Proofs -- 9 Unbounded Self-Adjoint Operators -- 10 The Spectral Theorem for Unbounded Self-Adjoint Operators -- 11 The Harmonic Oscillator -- 12 The Uncertainty Principle -- 13 Quantization Schemes for Euclidean Space -- 14 The Stone–von Neumann Theorem -- 15 The WKB Approximation -- 16 Lie Groups, Lie Algebras, and Representations -- 17 Angular Momentum and Spin -- 18 Radial Potentials and the Hydrogen Atom -- 19 Systems and Subsystems, Multiple Particles -- V Advanced Topics in Classical and Quantum Mechanics -- 20 The Path-Integral Formulation of Quantum Mechanics -- 21 Hamiltonian Mechanics on Manifolds -- 22 Geometric Quantization on Euclidean Space -- 23 Geometric Quantization on Manifolds -- A Review of Basic Material -- References. - Index.
520 _aAlthough ideas from quantum physics play an important role in many parts of modern mathematics, there are few books about quantum mechanics aimed at mathematicians. This book introduces the main ideas of quantum mechanics in language familiar to mathematicians. Readers with little prior exposure to physics will enjoy the book's conversational tone as they delve into such topics as the Hilbert space approach to quantum theory; the Schrödinger equation in one space dimension; the Spectral Theorem for bounded and unbounded self-adjoint operators; the Stone–von Neumann Theorem; the Wentzel–Kramers–Brillouin approximation; the role of Lie groups and Lie algebras in quantum mechanics; and the path-integral approach to quantum mechanics. The numerous exercises at the end of each chapter make the book suitable for both graduate courses and independent study. Most of the text is accessible to graduate students in mathematics who have had a first course in real analysis, covering the basics of L2 spaces and Hilbert spaces.  The final chapters introduce readers who are familiar with the theory of manifolds to more advanced topics, including geometric quantization.
650 0 _aMathematical physics.
650 0 _aQuantum physics.
650 0 _aFunctional analysis.
650 0 _aTopological groups.
650 0 _aLie groups.
650 0 _aPhysics.
650 1 4 _aMathematical Physics.
_0http://scigraph.springernature.com/things/product-market-codes/M35000
650 2 4 _aMathematical Applications in the Physical Sciences.
_0http://scigraph.springernature.com/things/product-market-codes/M13120
650 2 4 _aQuantum Physics.
_0http://scigraph.springernature.com/things/product-market-codes/P19080
650 2 4 _aFunctional Analysis.
_0http://scigraph.springernature.com/things/product-market-codes/M12066
650 2 4 _aTopological Groups, Lie Groups.
_0http://scigraph.springernature.com/things/product-market-codes/M11132
650 2 4 _aMathematical Methods in Physics.
_0http://scigraph.springernature.com/things/product-market-codes/P19013
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
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776 0 8 _iPrinted edition:
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776 0 8 _iPrinted edition:
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830 0 _aGraduate Texts in Mathematics,
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856 4 0 _uhttps://doi.org/10.1007/978-1-4614-7116-5
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