## Applications of Group Theory in Quantum MechanicsGeared toward postgraduate students, theoretical physicists, and researchers, this advanced text explores the role of modern group-theoretical methods in quantum theory. The authors based their text on a physics course they taught at a prominent Soviet university. Readers will find it a lucid guide to group theory and matrix representations that develops concepts to the level required for applications. The text's main focus rests upon point and space groups, with applications to electronic and vibrational states. Additional topics include continuous rotation groups, permutation groups, and Lorentz groups. A number of problems involve studies of the symmetry properties of the Schroedinger wave function, as well as the explanation of "additional" degeneracy in the Coulomb field and certain subjects in solid-state physics. The text concludes with an instructive account of problems related to the conditions for relativistic invariance in quantum theory. |

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Applications of Group Theory in Quantum Mechanics M. I. Petrashen,J. L. Trifonov Limited preview - 2013 |

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angle angular momentum antisymmetric applications arbitrary atom axis basis vectors belonging Brillouin zone Chapter characters cible representations classical complex conjugate components configuration consequently consider contains corresponding cosets crystal decomposed decomposition defined denote determine diagonal dimensional direct product displacements eigenfunctions eigenvalue eigenvectors electron element g energy levels equal equivalent fact finite group follows given group G Hamiltonian hence identity representation infinitesimal matrices infinitesimal operators invariant inversion irreducible repre irreducible representations lattice vector linear combinations Lorentz group matrix elements molecule multiplication normal coordinates nuclei obtain orthogonal oscillator parameters particles permutation group perturbation point group problem quantum mechanics quantum number readily verified reducible representation matrices rotation group Schroedinger equation selection rules sentations space group spin function spinor sponding sub-spaces sub—group suppose symmetry group tation tensor theorem tion transform in accordance unit element unit matrix unit vectors unitary wave function written Young's tableau zero