Group Theory and Its Applications

Group Theory and Its Applications

Volume II

1st Edition - January 28, 1971

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  • Editor: Ernest M. Loebl
  • eBook ISBN: 9781483263786

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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


    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


    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


    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


    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


    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


    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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