M. I. Petrashen

  • Applications of Group Theory in Quantum Mechanics

    M. I. Petrashen, E. D. Trifanov, and J. L. Martin

    This book is intended for theoretical physicists with a desire to understand the value of modern group-theoretical methods in quantum theory. The theory of groups and of their matrix representations of the invariance group of a Hamiltonian and the eigenvalue degeneracy is obtained.

    Once developed, the theory is applied to a variety of typical physical situations, usually quantum mechanical situations, usually quantum mechanical in nature, though attention is often given to classical systems with the same symmetries. The principal classes of groups considered are the point groups and space groups, with applications to the electric and vibrational states of molecules and crystals, respectively; the continuous rotation groups, indispensable to a proper treatment of quantum angular momentum and the Clebsch-Gordan coefficients; and the permutation groups, applied in particular to systems of many identical particles, with due account is given of the Lorentz group for special relativity and of the Dirac equation for the relativistic electron. Also included is a discussion of perturbation theory and selection rules.

    The course is presented at the postgraduate (or perhaps advanced undergraduate) level. A knowledge of original quantum mechanics is assumed; in all other respects, the book is self-contained.

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