The Theory of Groups and Quantum Mechanics

Couverture
Courier 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
BIBLIOGRAPHY
399
113
402
LIST OF OPERATIONAL SYMBOLS
409
116
412
123
415
136
417
157
420
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À propos de l'auteur (1950)

Along with his fundamental contributions to most branches of mathematics, Hermann Weyl (1885-1955) took a serious interest in theoretical physics. In addition to teaching in Zürich, Göttingen, and Princeton, Weyl worked with Einstein on relativity theory at the Institute for Advanced Studies.

Hermann Weyl: The Search for Beautiful Truths
One of the most influential mathematicians of the twentieth century, Hermann Weyl (1885–1955) was associated with three major institutions during his working years: the ETH Zurich (Swiss Federal Institute of Technology), the University of Gottingen, and the Institute for Advanced Study in Princeton. In the last decade of Weyl's life (he died in Princeton in 1955), Dover reprinted two of his major works, The Theory of Groups and Quantum Mechanics and Space, Time, Matter. Two others, The Continuum and The Concept of a Riemann Surface were added to the Dover list in recent years.

In the Author's Own Words:
"My work always tried to unite the truth with the beautiful, but when I had to choose one or the other, I usually chose the beautiful."

"We are not very pleased when we are forced to accept mathematical truth by virtue of a complicated chain of formal conclusions and computations, which we traverse blindly, link by link, feeling our way by touch. We want first an overview of the aim and of the road; we want to understand the idea of the proof, the deeper context."

"A modern mathematical proof is not very different from a modern machine, or a modern test setup: the simple fundamental principles are hidden and almost invisible under a mass of technical details." — Hermann Weyl

Critical Acclaim for Space, Time, Matter:
"A classic of physics . . . the first systematic presentation of Einstein's theory of relativity." — British Journal for Philosophy and Science




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