Group Theory and Its Applications

List of ContributorsPrefaceContents of Volume IThe 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 ReferencesSymmetry 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 ReferencesDynamical 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 ReferencesSymmetry 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 ReferencesGalilei 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 ReferencesAuthor IndexSubject Index