Quantum Theory for Mathematicians (inbunden)
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Inbunden (Hardback)
Antal sidor
2013 ed.
Springer-Verlag New York Inc.
36 schwarz-weiße Abbildungen
2 Illustrations, color; 28 Illustrations, black and white; XVI, 554 p. 30 illus., 2 illus. in color.
241 x 165 x 33 mm
975 g
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1 Hardback
Quantum Theory for Mathematicians (inbunden)

Quantum Theory for Mathematicians

Inbunden Engelska, 2013-06-19
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Although 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 Schroedinger 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.
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  • Lie Groups, Lie Algebras, and Representations

    Brian C Hall

    This textbook treats Lie groups, Lie algebras and their representations in an elementary but fully rigorous fashion requiring minimal prerequisites. In particular, the theory of matrix Lie groups and their Lie algebras is developed using only line...

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"This book is an introduction to quantum mechanics intended for mathematicians and mathematics students who do not have a particularly strong background in physics. ... A well-qualified graduate student can learn a lot from this book. I found it to be clear and well organized, and I personally enjoyed reading it very much." (David S. Watkins, SIAM Review, Vol. 57 (3), September, 2015) "This textbook is meant for advanced studies on quantum mechanics for a mathematical readership. The exercises at the end of each chapter make the book especially valuable." (A. Winterhof, Internationale Mathematischen Nachrichten, Issue 228, 2015) "There are a few textbooks on quantum theory for mathematicians who are alien to the physical culture ... but this modest textbook will surely find its place. All in all, the book is well written and accessible to any interested mathematicians and mathematical graduates." (Hirokazu Nishimura, zbMATH, Vol. 1273, 2013)

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Brian C. Hall is a Professor of Mathematics at the University of Notre Dame.


1 The Experimental Origins of Quantum Mechanics.- 2 A First Approach to Classical Mechanics.- 3 A First Approach to Quantum Mechanics.- 4 The Free Schroedinger 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.