Loebl Group Theory and Its Applications

Volume II
1. Auflage 2014
ISBN: 978-1-4832-6378-6
Verlag: Elsevier Science & Techn.
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, 326 Seiten, Web PDF

Group Theory and its Applications, Volume II covers the two broad areas of applications of group theory, namely, all atomic and molecular phenomena, as well as all aspects of nuclear structure and elementary particle theory. This volume contains five chapters and begins with the representation and tensor operators of the unitary groups. The next chapter describes wave equations, both Schrödinger's and Dirac's for a wide variety of potentials. These topics are followed by discussions of the applications of dynamical groups in dealing with bound-state problems of atomic and molecular physics. A chapter explores the connection between the physical constants of motion and the unitary group of the Hamiltonian, the symmetry adaptation with respect to arbitrary finite groups, and the Dixon method for computing irreducible characters without the occurrence of numerical errors. The last chapter deals with the study of the extension, representation, and applications of Galilei group. This book will prove useful to mathematicians, practicing engineers, and physicists.

Autoren/Hrsg.

Loebl, Ernest M.

Inhaltsverzeichnis

1;Front Cover;1
2;Group Theory and its Applications;4
3;Copyright Page;5
4;Table of Contents;6
5;List of Contributors;8
6;Preface;10
7;Contents of Volume I;14
8;Chapter 1. The Representations and Tensor Operators of the Unitary Groups U(n);16
8.1;I. Introduction: The Connection between the Representation Theory of S(n) and That of U(n), and Other Preliminaries;16
8.2;II. The Group SU(2) and Its Representations;36
8.3;III. The Matrix Elements for the Generators of U(n);42
8.4;IV. Tensor Operators and Wigner Coefficients on the Unitary Groups;60
8.5;REFERENCES;86
9;Chapter 2. Symmetry and Degeneracy;90
9.1;I. Introduction;90
9.2;II. Symmetry of the Hydrogen Atom;95
9.3;III. Symmetry of the Harmonic Oscillator;99
9.4;IV. Symmetry of Tops and Rotators;102
9.5;V. Bertrand's Theorem;106
9.6;VI. Non-Bertrandian Systems;110
9.7;VII. Cyclotron Motion;113
9.8;VIII. The Magnetic Monopole;116
9.9;IX. Two Coulomb Centers;120
9.10;X. Relativistic Systems;124
9.11;XI. Zitterbewegung;130
9.12;XII. Dirac Equation for the Hydrogen Atom;135
9.13;XIII. Other Possible Systems and Symmetries;140
9.14;XIV. Universal Symmetry Groups;144
9.15;XV. Summary;149
9.16;Acknowledgments;151
9.17;REFERENCES;152
10;Chapter 3. Dynamical Groups in Atomic and Molecular Physics;160
10.1;I. Introduction;160
10.2;II. The Second Vector Constant of Motion in Kepler Systems;162
10.3;III. The Four-Dimensional Orthogonal Group and the Hydrogen Atom;165
10.4;IV. Generalization of Fock's Equation: O(5) as a Dynamical Noninvariance Group;175
10.5;V. Symmetry Breaking in Helium;185
10.6;VI. Symmetry Breaking in First-Row Atoms;191
10.7;VII. The Conformai Group and One-Electron Systems;200
10.8;VIII. Conclusion;210
10.9;Acknowledgments;211
10.10;REFERENCES;211
11;Chapter 4. Symmetry Adaptation of Physical States by Means of Computers;214
11.1;I. Introduction;214
11.2;II. Constants of Motion and the Unitary Group of the Hamiltonian;214
11.3;III. Separation of Hilbert Space with Respect to the Constants of Motion;219
11.4;IV. Dixon's Method for Computing Irreducible Characters;221
11.5;V. Computation of Irreducible Matrix Representatives;226
11.6;VI. Group Theory and Computers;232
11.7;REFERENCES;234
12;Chapter 5. Galilei Group and Galilean Invariance;236
12.1;I. Introduction;237
12.2;II. The Galilei Group and Its Lie Algebra;239
12.3;III. The Extended Galilei Group and Lie Algebra;250
12.4;IV. Representations of the Galilei Groups;258
12.5;V. Applications to Classical Physics;269
12.6;VI. Applications to Quantum Physics;286
12.7;REFERENCES;311
13;Author Index;316
14;Subject Index;321