## Symmetry and its applications in science |

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### Contents

Group representations | 22 |

Basis vectors basis functions and quantum mechanics | 40 |

Crystal symmetry | 72 |

Copyright | |

8 other sections not shown

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### Common terms and phrases

angular momentum antisymmetric arbitrary axes basis functions basis vectors block form Bravais lattice Brillouin zone Cartesian centre chapter character table column contains crystal cyclic group defined degeneracy degenerate denotes determine diagonal dimension direct product direct product group direct product representation eigenfunctions eigenvalues eigenvectors electron empty lattice energy levels equal equivalent example fact given group D3 group operations group theory Hamiltonian Hence improper rotation integers invariant inversion irreducible representations labelled lattice vector linear combination matrix element matrix representation molecule multiplication table mutually orthogonal normal modes notation obtain obviously one-dimensional orbital perpendicular physical plane point group possess potential energy primitive cell projection operators properties quantum numbers rank tensor reducible rl(R rotation axis rotation group scalar product shown in Fig similarity transformation simple space group spin subgroup symmetrized basis symmetry elements symmetry operations tensor tion trace transition translation two-dimensional unitary vibrational zero