## Group Theory and Its Applications, Volume 2Group 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. |

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### Contents

1 | |

Chapter 2 Symmetry and Degeneracy | 75 |

Chapter 3 Dynamical Groups in Atomic and Molecular Physics | 145 |

Chapter 4 Symmetry Adaptation of Physical States by Means of Computers | 199 |

Chapter 5 Galilei Group and Galilean Invariance | 221 |

301 | |

306 | |

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### Common terms and phrases

accidental degeneracy angular momentum application arbitrary basis boson calculation canonical commutation relations commutation rules components conformal group conjugate constants coordinates corresponding defined denote determine diagonal dimension dimensional Dirac equation eigenvalues electron equivalent exponent expression fact factor finite Galilean invariance Galilean transformation Gel'fand pattern group theory Hamiltonian harmonic oscillator Hilbert space hydrogen atom hypersphere infinitesimal integral interaction irreducible representations isomorphic L. C. Biedenharn labels ladder operators Lie algebra Lie group linear magnetic field magnetic monopole Math monopole motion multiplicity nonrelativistic notation obtain orbits orthogonal particle permutation Phys physical Poincaré group problem properties pure Galilean transformations quantum field theory quantum mechanics quantum number reduced matrix element reduced Wigner operator relativistic representations of U(n result rotation group Runge vector Schrödinger equation Section space-time spherical symmetry spin SU(n subgroup symmetry group tensor operators theorem unitary groups variables wave equation wave functions Weyl Wigner coefficients