Quantum Mechanics: Symmetries

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9783540580805: Quantum Mechanics: Symmetries
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Greiner's lectures, which underlie these volumes, are internationally noted for their clarity, their completeness and for the effort that he has devoted to making physics an integral whole; his enthusiasm for his science is contagious and shines through almost every page. These volumes represent only a part of a unique and Herculean effort to make all of theoretical physics accessible to the interested student. Beyond that, they are of enormous value to the professional physicist and to all others working with quantum phenomena. Again and again the reader will find that, after dipping into a particular volume to review a specific topic, he will end up browsing, caught up by often fascinating new insights and developments with which he had not previously been familiar. Having used a number of Greiner's volumes in their original German in my teaching and research at Yale, I welcome these new and revised English translations and would recommend them enthusiastically to anyone searching for a coherent overview of physics.

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Contenuti:

1. Symmetries in Quantum Mechanics.- 1.1 Symmetries in Classical Physics.- 1.2 Spatial Translations in Quantum Mechanics.- 1.3 The Unitary Translation Operator.- 1.4 The Equation of Motion for States Shifted in Space.- 1.5 Symmetry and Degeneracy of States.- 1.6 Time Displacements in Quantum Mechanics.- 1.7 Mathematical Supplement: Definition of a Group.- 1.8 Mathematical Supplement: Rotations and their Group Theoretical Properties.- 1.9 An Isomorphism of the Rotation Group.- 1.9.1 Infinitesimal and Finite Rotations.- 1.9.2 Isotropy of Space.- 1.10 The Rotation Operator for Many-Particle States.- 1.11 Biographical Notes.- 2. Angular Momentum Algebra Representation of Angular Momentum Operators — Generators of SO(3).- 2.1 Irreducible Representations of the Rotation Group.- 2.2 Matrix Representations of Angular Momentum Operators.- 2.3 Addition of Two Angular Momenta.- 2.4 Evaluation of Clebsch-Gordan Coefficients.- 2.5 Recursion Relations for Clebsch-Gordan Coefficients.- 2.6 Explicit Calculation of Clebsch-Gordan Coefficients.- 2.7 Biographical Notes.- 3. Mathematical Supplement: Fundamental Properties of Lie Groups.- 3.1 General Structure of Lie Groups.- 3.2 Interpretation of Commutators as Generalized Vector Products, Lie’s Theorem, Rank of Lie Group.- 3.3 Invariant Subgroups, Simple and Semisimple Lie Groups, Ideals.- 3.4 Compact Lie Groups and Lie Algebras.- 3.5 Invariant Operators (Casimir Operators).- 3.6 Theorem of Racah.- 3.7 Comments on Multiplets.- 3.8 Invariance Under a Symmetry Group.- 3.9 Construction of the Invariant Operators.- 3.10 Remark on Casimir Operators of Abelian Lie Groups.- 3.11 Completeness Relation for Casimir Operators.- 3.12 Review of Some Groups and Their Properties.- 3.13 The Connection Between Coordianate Transformations and Transformations of Functions.- 3.14 Biographical Notes.- 4. Symmetry Groups and Their Physical Meaning -General Considerations.- 4.1 Biographical Notes.- 5. The Isospin Group (Isobaric Spin).- 5.1 Isospin Operators for a Multi-Nucleon System.- 5.2 General Properties of Representations of a Lie Algebra.- 5.3 Regular (or Adjoint) Representation of a Lie Algebra.- 5.4 Transformation Law for Isospin Vectors.- 5.5 Experimental Test of Isospin Invariance.- 5.6 Biographical Notes.- 6. The Hypercharge.- 6.1 Biographical Notes.- 7. The SU(3) Symmetry.- 7.1 The Groups U(n) and SU(n).- 7.1.1. The Generators of U(n) and SU(n).- 7.2 The Generators of SU(3).- 7.3 The Lie Algebra of SU(3).- 7.4 The Subalgebras of the SU(3)-Lie Algebra and the Shift Operators.- 7.5 Coupling of T-, U- and V-Multiplets.- 7.6 Quantitative Analysis of Our Reasoning.- 7.7 Further Remarks About the Geometric Form of an SU(3) Multiplet.- 7.8 The Number of States on Mesh Points on Inner Shells.- 8. Quarks and SU(3).- 8.1 Searching for Quarks.- 8.2 The Transformation Properties of Quark States.- 8.3 Construction of all SU(3) Multiplets from the Elementary Representations [3] and 3.- 8.4 Construction of the Representation D(p, q) from Quarks and Antiquarks.- 8.4.1. The Smallest SU(3) Representations.- 8.5 Meson Multiplets.- 8.6 Rules for the Reduction of Direct Product of SU(3) Multiplets.- 8.7 U-spin Invariance.- 8.8 Test of U-spin Invariance.- 8.9 The Gell-Mann-Okubo Mass Formula.- 8.10 The Clebsch-Gordan Coefficients of the SU(3).- 8.11 Quark Models with Inner Degrees of Freedom.- 8.12 The Mass Formula in SU(6).- 8.13 Magnetic Moments in the Quark Model.- 8.14 Excited Meson and Baryon States.- 8.14.1 Combinations of More Than Three Quarks.- 8.15 Excited States with Orbital Angular Momentum.- 9. Representations of the Permutation Group and Young Tableaux.- 9.1 The Permutation Group and Identical Particles.- 9.2 The Standard Form of Young Diagrams.- 9.3 Standard Form and Dimension of Irreducible Representations of the Permutation Group SN.- 9.4 The Connection Between SU(2) and S2.- 9.5 The Irreducible Representations of SU(n).- 9.6 Determination of the Dimension.- 9.7 The SU(n — 1) Subgroups of SU(n).- 9.8 Decomposition of the Tensor Product of Two Multiplets.- 10. Mathematical Excursion. Group Characters.- 10.1 Definition of Group Characters.- 10.2 Schur’s Lemmas.- 10.2.1 Schur’s First Lemma.- 10.2.2 Schur’s Second Lemma.- 10.3 Orthogonality Relations of Representations and Discrete Groups.- 10.4 Equivalence Classes.- 10.5 Orthogonality Relations of the Group Characters for Discrete Groups and Other Relations.- 10.6 Orthogonality Relations of the Group Characters for the Example of the Group D3.- 10.7 Reduction of a Representation.- 10.8 Criterion for Irreducibility.- 10.9 Direct Product of Representations.- 10.10 Extension to Continuous, Compact Groups.- 10.11 Mathematical Excursion: Group Integration.- 10.12 Unitary Groups.- 10.13 The Transition from U(N) to SU(N) for the Example SU(3).- 10.14 Integration over Unitary Groups.- 10.15 Group Characters of Unitary Groups.- 11. Charm and SU(4).- 11.1 Particles with Charm and the SU(4).- 11.2 The Group Properties of SU(4).- 11.3 Tables of the Structure Constants fijk and the Coefficients dijk for SU(4).- 11.4 Multiplet Structure of SU(4).- 11.5 Advanced Considerations.- 11.5.1 Decay of Mesons with Hidden Charm.- 11.5.2 Decay of Mesons with Open Charm.- 11.5.3 Baryon Multiplets.- 11.6 The Potential Model of Charmonium.- 11.7 The SU(4) [SU(8)] Mass Formula.- 11.8 The ? Resonances.- 12. Mathematical Supplement.- 12.1 Introduction.- 12.2 Root Vectors and Classical Lie Algebras.- 12.3 Scalar Products of Eigenvalues.- 12.4 Cartan-Weyl Normalization.- 12.5 Graphic Representation of the Root Vectors.- 12.6 Lie Algebra of Rank 1.- 12.7 Lie Algebras of Rank 2.- 12.8 Lie Algebras of Rank l > 2.- 12.9 The Exceptional Lie Algebras.- 12.10 Simple Roots and Dynkin Diagrams.- 12.11 Dynkin’s Prescription.- 12.12 The Cartan Matrix.- 12.13 Determination of all Roots from the Simple Roots.- 12.14 Two Simple Lie Algebras.- 12.15 Representations of the Classical Lie Algebras.- 13. Special Discrete Symmetries.- 13.1 Space Reflection (Parity Transformation).- 13.2 Reflected States and Operators.- 13.3 Time Reversal.- 13.4 Antiunitary Operators.- 13.5 Many-Particle Systems.- 13.6 Real Eigenfunctions.- 14. Dynamical Symmetries.- 14.1 The Hydrogen Atom.- 14.2 The Group SO(4).- 14.3 The Energy Levels of the Hydrogen Atom.- 14.4 The Classical Isotropic Oscillator.- 14.4.1 The Quantum Mechanical Isotropic Oscillator.- 15. Mathematical Excursion: Non-compact Lie Groups.- 15.1 Definition and Examples of Non-compact Lie Groups.- 15.2 The Lie Group SO(2,l).- 15.3 Application to Scattering Problems.

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Altre edizioni note dello stesso titolo

9783540780458: Quantum Mechanics: An Introduction

Edizione in evidenza

ISBN 10:  3540780459 ISBN 13:  9783540780458
Casa editrice: Springer Verlag, 2008
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9783540580799: QUANTUM MECHANICS . : AN INTRODUCTION

Spring..., 1994
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