
Group Theory and Its Applications
Volume II
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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.
Table of Contents
List of Contributors
Preface
Contents of Volume I
The Representations and Tensor Operators of the Unitary Groups U(n)
I. Introduction: The Connections Between the Representation Theory of S(n) and That of U(n), and Other Preliminaries
II. The Group SU(2) and Its Representations
III. The Matrix Elements for the Generators of U(n)
IV. Tensor Operators and Wigner Coefficients on the Unitary Groups
References
Symmetry and Degeneracy
I. Introduction
II. Symmetry of the Hydrogen Atom
III. Symmetry of the Harmonic Oscillator
IV. Symmetry of Tops and Rotators
V. Bertrand's Theorem
VI. Non-Bertrandian Systems
VII. Cyclotron Motion
VIII. The Magnetic Monopole
IX. Two Coulomb Centers
X. Relativistic Systems
XI. Zitterbewegung
XII. Dirac Equation for the Hydrogen Atom
XIII. Other Possible Systems and Symmetries
XIV. Universal Symmetry Groups
XV. Summary
References
Dynamical Groups in Atomic and Molecular Physics
I. Introduction
II. The Second Vector Constant of Motion in Kepler Systems
III. The Four-Dimensional Orthogonal Group and the Hydrogen Atom
IV. Generalization of Fock's Equation: O(5) as a Dynamical Noninvariance Group
V. Symmetry Breaking in Helium
VI. Symmetry Breaking in First-Row Atoms
VII. The Conformal Group and One-Electron Systems
VIII. Conclusion
References
Symmetry Adaptation of Physical States by Means of Computers
I. Introduction
II. Constants of Motion and the Unitary Group of the Hamiltonian
III. Separation of Hilbert Space with Respect to the Constants of Motion
IV. Dixon's Method for Computing Irreducible Characters
V. Computation of Irreducible Matrix Representatives
VI. Group Theory and Computers
References
Galilei Group and Galilean Invariance
I. Introduction
II. The Galilei Group and Its Lie Algebra
III. The Extended Galilei Group and Lie Algebra
IV. Representations of the Galilei Groups
V. Applications to Classical Physics
VI. Applications to Quantum Physics
References
Author Index
Subject Index
Product details
- No. of pages: 326
- Language: English
- Copyright: © Academic Press 1971
- Published: January 28, 1971
- Imprint: Academic Press
- eBook ISBN: 9781483263786
About the Editor
Ernest M. Loebl
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