Wigner Group Theory And Its Application To The Quantum Mechanics Of Atomic Spectra Pdf
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Group Theory
Group Theory and its Application to the Quantum Mechanics of Atomic Spectra describes the applications of group theoretical methods to problems of quantum mechanics with particular reference to atomic spectra. The manuscript first takes a look at vectors and matrices, generalizations, and principal axis transformation. Topics include principal axis transformation for unitary and Hermitian matrices; unitary matrices and the scalar product; linear independence of vectors; and real orthogonal and symmetric matrices. The publication also ponders on the elements of quantum mechanics, perturbation theory, and transformation theory and the bases for the statistical interpretation of quantum mechanics. The book discusses abstract group theory and invariant subgroups, including theorems of finite groups, factor group, and isomorphism and homomorphism. The text also reviews the algebra of representation theory, rotation groups, three-dimensional pure rotation group, and characteristics of atomic spectra. Discussions focus on eigenvalues and quantum numbers, spherical harmonics, and representations of the unitary group. The manuscript is a valuable reference for readers interested in the applications of group theoretical methods.
Classical Mechanics and Quantum Mechanics: An Historic-Axiomatic Approach
Author: Peter Enders
language: en
Publisher: Bentham Science Publishers
Release Date: 2019-09-05
This unique textbook presents a novel, axiomatic pedagogical path from classical to quantum physics. Readers are introduced to the description of classical mechanics, which rests on Euler’s and Helmholtz’s rather than Newton’s or Hamilton’s representations. Special attention is given to the common attributes rather than to the differences between classical and quantum mechanics. Readers will also learn about Schrödinger’s forgotten demands on quantization, his equation, Einstein’s idea of ‘quantization as selection problem’. The Schrödinger equation is derived without any assumptions about the nature of quantum systems, such as interference and superposition, or the existence of a quantum of action, h. The use of the classical expressions for the potential and kinetic energies within quantum physics is justified. Key features: · Presents extensive reference to original texts. · Includes many details that do not enter contemporary representations of classical mechanics, although these details are essential for understanding quantum physics. · Contains a simple level of mathematics which is seldom higher than that of the common (Riemannian) integral. · Brings information about important scientists · Carefully introduces basic equations, notations and quantities in simple steps This book addresses the needs of physics students, teachers and historians with its simple easy to understand presentation and comprehensive approach to both classical and quantum mechanics..
Applying Mathematics
How is that when scientists need some piece of mathematics through which to frame their theory, it is there to hand? Bueno and French offer a new approach to the puzzle of the applicability of mathematics, through a detailed examination of a series of case studies from the history of twentieth-century physics.