Group Theory and Its Applications: Volume II, Volume 2Ernest M. Loebl 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. |
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 | |
Common terms and phrases
a₁ accidental degeneracy angular momentum arbitrary basis boson calculation canonical classical mechanics commutation relations commutation rules components conformal group conjugate constants coordinates corresponding defined denote determine diagonal dimension dimensional Dirac equation E. P. Wigner eigenvalues electron equivalent exponent fact factor finite Fock's Galilean invariance Galilean transformation Gel'fand pattern group theory H₁ Hamiltonian harmonic oscillator Hilbert space hydrogen atom hypersphere infinitesimal integral irreducible representations isomorphic K₁ L. C. Biedenharn labels ladder operators Lévy-Leblond Lie algebra Lie group linear magnetic field Math monopole motion multiplicity nonrelativistic notation obtain orbits P₁ particle permutation Phys physical Poincaré group problem properties pure Galilean transformations quantum mechanics quantum number reduced Wigner operator relativistic representations of U(n result rotation group Schrödinger equation Section space-time spin SU(n subgroup symmetry group tensor operators theorem unimodular unitary groups variables wave equation wave functions Weyl Wigner coefficients