Symmetries In Quantum Mechanics And Statistical Physics
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Symmetries in Quantum Mechanics and Statistical Physics
This book collects contributions to the Special Issue entitled "Symmetries in Quantum Mechanics and Statistical Physics" of the journal Symmetry. These contributions focus on recent advancements in the study of PT-invariance of non-Hermitian Hamiltonians, the supersymmetric quantum mechanics of relativistic and non-relativisitc systems, duality transformations for power-law potentials and conformal transformations. New aspects on the spreading of wave packets are also discussed.
A First Course on Symmetry, Special Relativity and Quantum Mechanics
This book provides an in-depth and accessible description of special relativity and quantum mechanics which together form the foundation of 21st century physics. A novel aspect is that symmetry is given its rightful prominence as an integral part of this foundation. The book offers not only a conceptual understanding of symmetry, but also the mathematical tools necessary for quantitative analysis. As such, it provides a valuable precursor to more focused, advanced books on special relativity or quantum mechanics. Students are introduced to several topics not typically covered until much later in their education.These include space-time diagrams, the action principle, a proof of Noether's theorem, Lorentz vectors and tensors, symmetry breaking and general relativity. The book also provides extensive descriptions on topics of current general interest such as gravitational waves, cosmology, Bell's theorem, entanglement and quantum computing. Throughout the text, every opportunity is taken to emphasize the intimate connection between physics, symmetry and mathematics.The style remains light despite the rigorous and intensive content. The book is intended as a stand-alone or supplementary physics text for a one or two semester course for students who have completed an introductory calculus course and a first-year physics course that includes Newtonian mechanics and some electrostatics. Basic knowledge of linear algebra is useful but not essential, as all requisite mathematical background is provided either in the body of the text or in the Appendices. Interspersed through the text are well over a hundred worked examples and unsolved exercises for the student.
Symmetry and Quantum Mechanics
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 SL(sub[2])(C) is the universal cover of SO(sup[+]) (1, 3) -- 9.4 The Dirac equation -- Appendix 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 -- Bibliography -- Index