## The Theory of Groups and Quantum MechanicsThis landmark among mathematics texts applies group theory to quantum mechanics, first covering unitary geometry, quantum theory, groups and their representations, then applications themselves — rotation, Lorentz, permutation groups, symmetric permutation groups, and the algebra of symmetric transformations. |

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### Contents

QUANTUM THEory | 41 |

Collision Phenomena | 70 |

The Dynamical Law Transition Probabilities | 80 |

Perturbation Theory | 86 |

Commutation Rules Canonical Transformations | 93 |

Atom in Interaction with Radiation | 103 |

GRoups AND THEIR REPRESENTATIons | 110 |

Formal Processes ClebschGordan Series | 123 |

2 | 163 |

Applicarion of THE THEory of Groups ro QuANTUM MechAN1cs | 180 |

THE SYMMETRic PERMUTATION GRoup AND THE ALGFBRA of SYM | 277 |

Determination of the Primitive Characters of u and m | 377 |

17 Calculation of Volume on u | 386 |

Affendix | 393 |

409 | |

410 | |

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### Common terms and phrases

accordance algebra anti-symmetric arbitrary aſs associated assume atom azimuthal quantum belongs character characteristic numbers classical coefficients column commutation rules completely reduced components conjugate consequently consider consists constitute contained defined denote determinant diagonal dimensionality electron energy levels equivalent expressed fact factor follows formula function fundamental given group manifold Hence Hermitian form Hermitian operator idempotent idempotent elements induced inequivalent infinitesimal integral irreducible constituents irreducible representation linear correspondence linear transformations linearly independent matrix momentum multiplication n-dimensional non-vanishing normal co-ordinate system obtained operator order f orthogonal permutation group perturbation physical polynomial primitive quantity quantization quantum mechanics quantum theory regular representation replacing repre respect restricting result rotation group rows scalar sentation spin sub-group symmetric transformations symmetry class symmetry pattern system space tensors of order theorem tion transition unit unitary transformation values vanish variables vector space wave Zeeman effect