The Theory of Groups and Quantum MechanicsCourier Corporation, 1 janv. 1950 - 422 pages This 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. |
Table des matières
UNITARY GEOMETRY 1 The ndimensional Vector Space | 1 |
Linear Correspondences | 6 |
Matrix Calculus | 8 |
Unitary Geometry and Hermitian Forms 3 The Dual Vector Space | 12 |
Transformation to Principal Axes | 25 |
Infinitesimal Unitary Transformations | 31 |
Remarks on dimensional Space 5 | 33 |
NNNGH 12 | 35 |
Representation by Rotations of Ray Space | 180 |
APPLICATION OF THE THEORY OF GROUPS TO QUANTUM MECHANICS | 185 |
Simple States and Term Analysis Examples | 191 |
Selection and Intensity Rules | 197 |
The Spinning Electron Multiplet Structure and Anomalous Zeeman Effect | 202 |
B The Lorentz Group 5 Relativistically Invariant Equations of Motion of an Electron | 210 |
Energy and Momentum Remarks on the Interchange of Past and Future | 218 |
Electron in Spherically Symmetric Field | 227 |
QUANTUM THEORY | 41 |
Physical Foundations | 47 |
The de Broglie Waves of a Particle | 48 |
Schrödingers Wave Equation The Harmonic Oscillator | 54 |
Spherical Harmonics | 60 |
Electron in Spherically Symmetric Field Directional Quan tization | 63 |
Collision Phenomena | 73 |
The Conceptual Structure of Quantum Mechanics | 74 |
The Dynamical Law Transition Probabilities | 80 |
Perturbation Theory | 86 |
The Problem of Several Bodies Product Space | 89 |
Commutation Rules Canonical Transformations | 93 |
Motion of a Particle in an Electromagnetic Field Effect and Stark Effect | 98 |
Atom in Interaction with Radiation | 103 |
GROUPS AND THEIR REPRESENTATIONS | 110 |
Transformation Groups 2 Abstract Groups and their Realization | 115 |
Subgroups and Conjugate Classes 63 70 74 80 86 89 93 | 116 |
Representation of Groups by Linear Transformations | 120 |
Formal Processes ClebschGordan Series | 123 |
The JordanHölder Theorem and its Analogues | 131 |
Unitary Representations | 136 |
Rotation and Lorentz Groups | 149 |
Character of a Representation | 151 |
Schurs Lemma and Burnsides Theorem | 153 |
Orthogonality Properties of Group Characters | 157 |
Extension to Closed Continuous Groups | 160 |
110 | 163 |
The Algebra of a Group | 165 |
Invariants and Covariants | 170 |
Remarks on Lies Theory of Continuous Groups of Trans formations | 175 |
Selection Rules Fine Structure | 232 |
The Permutation Group 9 Resonance between Equivalent Individuals | 238 |
The Pauli Exclusion Principle and the Structure of the Periodic Table | 242 |
The Problem of Several Bodies and the Quantization of the Wave Equation | 246 |
Quantization of the MaxwellDirac Field Equations | 253 |
The Energy and Momentum Laws of Quantum Physics Relativistic Invariance | 264 |
Quantum Kinematics 14 Quantum Kinematics as an Abelian Group of Rotations | 272 |
Derivation of the Wave Equation from the Commutation Rules | 277 |
THE SYMMETRIC PERMUTATION GROUP AND THE ALGEBRA OF SYM METRIC TRANSFORMATIONS | 281 |
Symmetry Classes of Tensors | 286 |
Invariant Subspaces in Group Space | 291 |
Invariant Subspaces in Tensor Space | 296 |
Fields and Algebras | 302 |
Representations of Algebras | 304 |
Constructive Reduction of an Algebra into Simple Matric Algebras | 309 |
B Extension of the Theory and Physical Applications 8 The Characters of the Symmetric Group and Equivalence Degeneracy in Quantum Mechanics | 319 |
Relation between the Characters of the Symmetric Per mutation and Affine Groups | 326 |
Direct Product Subgroups | 332 |
Perturbation Theory for the Construction of Molecules | 339 |
The Symmetry Problem of Quantum Theory | 347 |
APPENDIX | 393 |
399 | |
113 | 402 |
LIST OF OPERATIONAL SYMBOLS | 409 |
116 | 412 |
415 | |
417 | |
420 | |
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Expressions et termes fréquents
accordance algebra anti-symmetric arbitrary 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 determined dimensionality e₁ e₂ electron energy levels equivalent expressed f₁ fact factor follows formula function fundamental given group manifold h₁ h₂ Hence Hermitian form Hermitian operator idempotent idempotent elements induced infinitesimal integral irreducible constituents irreducible representation k₁ linear correspondence linear transformations linearly independent matrix momentum multiplication n-dimensional normal co-ordinate system obtained operator order ƒ orthogonal p₁ P₂ permutation permutation group perturbation physical polynomial primitive quantities quantum mechanics quantum theory regular representation replacing repre representation h respect rotation group rows scalar sentation spin sub-group symmetric transformations symmetry pattern system space tensors of order theorem tion unit unitary representation unitary transformation values vanish variables vector space wave Zeeman effect