Quantum Mechanics: Symmetries
With 127 Worked Examples and Problems
(Sprache: Englisch)
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...
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Produktinformationen zu „Quantum Mechanics: Symmetries “
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.
Klappentext zu „Quantum Mechanics: Symmetries “
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.
Inhaltsverzeichnis zu „Quantum Mechanics: Symmetries “
1. Symmetries in Quantum Mechanics1.1 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
... mehr
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
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
... weniger
Autoren-Porträt von Walter Greiner, Berndt Müller
Prof. Dr. rer. nat. Dr. h. c. mult. Walter Greiner, geb. Oktober 1935 im Thüringer Wald, Promotion 1961 in Freiburg im Breisgau, 1962-64 Assistent Professor an der University of Maryland, seit 1964/65 ordentlicher Professor für Theoretische Physik der Johann Wolfgang Goethe-Universität Frankfurt am Main und Direktor des Instituts für Theoretische Physik. Gastprofessuren unter anderem an der Florida State University, University of Virginia, Los Alamos Scientific Laboratory, University of California Berkeley, Oak Ridge National Laboratory, University of Melbourne, Yale University, Vanderbilt University, University of Arizona. Hauptarbeitsgebiete sind die Struktur und Dynamik der elementaren Materie (Quarks, Gluonen, Mesonen, Baryonen, Atomkerne), Schwerionenphysik, Feldtheorie (Quantenelektrodynamik, Eichtheorie der schwachen Wechselwirkung, Quantenchromodynamik, Theorie der Gravitation), Atomphysik.974 Empfänger des Max-Born-Preises und der Max-Born-Medaille des Institute of Physics (London) und der Deutsche Physikalische Gesellschaft, 1982 des Otto-Hahn-Preises der Stadt Frankfurt am Main, 1998 der Alexander von Humboldt-Medaille, 1999 Officier dans l'Ordre des Palmes Academiques.
Inhaber zahlreicher Ehrendoktorwürden (unter anderem der University of Witwatersrand, Johannesburg, der Universite Louis Pasteur Strasbourg, der UNAM Mexico, der Universitäten Bucharest, Tel Aviv, Nantes, St. Petersburg, Moskau, Debrecen, Dubna und anderen) sowie Ehrenprofessuren (University of Bejing, China, und Jilin University Changchun, China) und Ehrenmitglied vieler Akademien.
Bibliographische Angaben
- Autoren: Walter Greiner , Berndt Müller
- 2nd revidierte ed. 1994. 3rd printing 2001, 526 Seiten, 1 Schwarz-Weiß-Abbildungen, Maße: 18,9 x 24,6 cm, Kartoniert (TB), Englisch
- Mitarbeit: Bromley, David A.
- Verlag: Springer
- ISBN-10: 3540580808
- ISBN-13: 9783540580805
- Erscheinungsdatum: 09.10.2001
Sprache:
Englisch
Rezension zu „Quantum Mechanics: Symmetries “
From the reviews: "a ] A student who works through the examples will be in an excellent position to calculate the consequences of symmetry in atomic, nuclear and particles systems." American Journal of Physics
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