The Theory of Groups and Quantum Mechanics

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Courier Corporation, 1950 - Mathematics - 422 pages
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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.
 

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Contents

UNITARY GEOMETRY i
1
Linear Correspondences Matrix Calculus
5
The Dual Vector Space
12
Unitary Geometry and Hermitian Forms
15
Transformation to Principal Axes
21
Infinitesimal Unitary Transformations
27
Remarks on odimensional Space
31
It QUANTUM THEORY
41
Rotation and Lorentz Groups
140
Character of a Representation
150
Schurs Lemma and Bumsides Theorem
152
Orthogonality Properties of Group Characters
157
APPLICATION or THB THEORY OF GROUPS TO QUANTUM MECHANICS
185
B The Lorentz Group
210
Energy and Momentum Remarks on the Interchange of Past
218
Electron in Spherically Symmetric Field
227

The de Brogiie Waves of a Particle
48
Schrodingers Wave Equation The Harmonic Oscillator
54
Spherical Harmonics
60
Electron in Spherically Symmetric Field Directional Quan tization
63
Collision Phenomena
70
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 Zeeman Effect and Stark Effect
98
Atom in Interaction with Radiation
102
GROUPS AND THEIR REPRESENTATIONS I IO 1 Transformation Groups
110
Abstract Groups and their Realization
113
Subgroups and Conjugate Classes
116
Representation of Groups by Linear Transformations
120
Formal Processes ClebschGordan Series
123
The JordanHolder Theorem and its Analogues
131
Unitary Representations
136
The Permutation Group
238
The Problem of Several Bodies and the Quantization
246
Quantization of the MaxwellDirac Field Equations
253
The Energy and Momentum Laws of Quantum Physics
264
Quantum Kinematics
272
THE SYMMETRIC PERMUTATION GROUP AND THE ALGKBRA OF SYM
281
Invariant Subspaces in Group Space
291
Fields and Algebras
302
Constructive Reduction of an Algebra into Simple Matric
309
The Characters of the Symmetric Group and Equivalence
319
Relation between the Characters of the Symmetric Per
326
Direct Product Subgroups
332
Perturbation Theory for the Construction of Molecules
339
The Symmetry Problem of Quantum Theory
347
AriNDix
393
BIBLIOGRAPHY
399
LIST OF OPERATIONAL SYMBOLS
409
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About the author (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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