Symmetry and quantum mechanics / Scott Corry, Lawrence University, Appleton, Wisconsin, USA

Author:: Corry, Scott
Published:: Boca Raton : CRC Press, Taylor & Francis Group, [2017]
Physical Description:: xxv, 256 pages : illustrations ; 25 cm.

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Monographs and research notes in mathematics

Contents:

Machine generated contents note: I. Spin -- 1. Physical Space -- 1.1. Modeling space -- 1.2. Real linear operators and matrix groups -- 1.3. SO(3) is the group of rotations -- 2. Spinor Space -- 2.1. Angular momentum in classical mechanics -- 2.2. Modeling spin -- 2.3. Complex linear operators and matrix groups -- 2.4. The geometry of SU(2) -- 2.4.1. The tangent space to the circle U(1) = S1 -- 2.4.2. The tangent space to the sphere SU(2) = S3 -- 2.4.3. The exponential of a matrix -- 2.4.4. SU{2) is the universal cover of SO(3) -- 2.5. Back to spinor space -- 3. Observables and Uncertainty -- 3.1. Spin observables -- 3.2. The Lie algebra su(2) -- 3.3. Commutation relations and uncertainty -- 3.4. Some related Lie algebras -- 3.4.1. Warmup: The Lie algebra u(1) -- 3.4.2. The Lie algebra sl2(C) -- 3.4.3. The Lie algebra u(2) -- 3.4.4. The Lie algebra gl2(C) -- 4. Dynamics -- 4.1. Time-independent external fields -- 4.2. Time-dependent external fields -- 4.3. The energy-time uncertainty principle -- 4.3.1. Conserved quantities -- 5. Higher Spin -- 5.1. Group representations -- 5.2. Representations of SU(2) -- 5.3. Lie algebra representations -- 5.4. Representations of su(2)c = sl2(C) -- 5.5. Spin-s particles -- 5.6. Representations of SO(3) -- 5.6.1. The so(3)-action -- 5.6.2. Comments about analysis -- 6. Multiple Particles -- 6.1. Tensor products of representations -- 6.2. The Clebsch-Gordan problem -- 6.3. Identical particles -- spin only -- II. Position & Momentum -- 7. A One-Dimensional World -- 7.1. Position -- 7.2. Momentum -- 7.3. The Heisenberg Lie algebra and Lie group -- 7.3.1. The meaning of the Heisenberg group action -- 7.4. Time-evolution -- 7.4.1. The free particle -- 7.4.2. The infinite square well -- 7.4.3. The simple harmonic oscillator -- 8. A Three-Dimensional World -- 8.1. Position -- 8.2. Linear momentum -- 8.2.1. The Heisenberg group H3 and its algebra h3 -- 8.3. Angular momentum -- 8.4. The Lie group G = H3 x SO(3) and its Lie algebra g -- 8.5. Time-evolution -- 8.5.1. The free particle -- 8.5.2. The three-dimensional harmonic oscillator -- 8.5.3. Central potentials -- 8.5.4. The infinite spherical well -- 8.6. Two-particle systems -- 8.6.1. The Coulomb potential -- 8.7. Particles with spin -- 8.7.1. The hydrogen atom -- 8.8. Identical particles -- 9. Toward a Relativistic Theory -- 9.1. Galilean relativity -- 9.2. Special relativity -- 9.3. SL2(C) is the universal cover of SO+(1, 3) -- 9.4. The Dirac equation -- A. Appendices -- A.1. Linear algebra -- A.1.1. Vector spaces and linear transformations -- A.1.2. Inner product spaces and adjoints -- A.2. Multivariable calculus -- A.3. Analysis -- A.3.1. Hilbert spaces and adjoints -- A.3.2. Some big theorems -- A.4. Solutions to selected exercises.

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ISBN:

9781498701167 (hardback)
1498701167 (hardback)
9781498701174 (e-book)

Note:

"A Chapman & Hall book."

Bibliography Note:

Includes bibliographical references and index.

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