The Theory of Groups and Quantum Mechanics

Front Cover
Courier Corporation, Jan 1, 1950 - Mathematics - 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.
 

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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
List of OPERATIONAL SYMBols
409
185
410

The JordanHölder Theorem and its Analogues
131
Rotation and Lorentz Groups
140
Character of a Representation
150

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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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