Advanced Calculus And Its Applications In Variational Quantum Mechanics And Relativity Theory
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Advanced Calculus and its Applications in Variational Quantum Mechanics and Relativity Theory
The first part of this book reviews some key topics on multi-variable advanced calculus. The approach presented includes detailed and rigorous studies on surfaces in Rn which comprises items such as differential forms and an abstract version of the Stokes Theorem in Rn. The conclusion section introduces readers to Riemannian geometry, which is used in the subsequent chapters. The second part reviews applications, specifically in variational quantum mechanics and relativity theory. Topics such as a variational formulation for the relativistic Klein-Gordon equation, the derivation of a variational formulation for relativistic mechanics firstly through (semi)-Riemannian geometry are covered. The second part has a more general context. It includes fundamentals of differential geometry. The later chapters describe a new interpretation for the Bohr atomic model through a semi-classical approach. The book concludes with a classical description of the radiating cavity model in quantum mechanics.
General Relativity and Matter
Author: M. Sachs
language: en
Publisher: Springer Science & Business Media
Release Date: 2013-03-09
There exist essentially two levels of investigation in theoretical physics. One is primarily descriptive, concentrating as it does on useful phenomenological approaches toward the most economical classifications of large classes of experimental data on particular phenomena. The other, whose thrust is explanatory, has as its aim the formulation of those underlying hypotheses and their mathematical representations that are capable of furnishing, via deductive analysis, predictions - constituting the particulars of universals (the asserted laws)- about the phenomena under consideration. The two principal disciplines of contemporary theoretical physics - quantum theory and the theory of relativity - fall basically into these respective categories. General Relativity and Matter represents a bold attempt by its author to formulate, in as transparent and complete a way as possible, a fundamental theory of matter rooted in the theory of relativity - where the latter is viewed as providing an explanatory level of understanding for probing the fundamental nature ofmatter indomainsranging all the way fromfermis and lessto light years and more. We hasten to add that this assertion is not meant to imply that the author pretends with his theory to encompass all ofphysics or even a tiny part of the complete objective understanding of our accessible universe. But he does adopt the philosophy that underlying all natural phenomena there is a common conceptualbasis,and then proceeds to investigate how far such a unified viewcan take us at its present stage of development.
An Introduction to Lebesgue Integration and Fourier Series
Author: Howard J. Wilcox
language: en
Publisher: Courier Corporation
Release Date: 1994-01-01
This book arose out of the authors' desire to present Lebesgue integration and Fourier series on an undergraduate level, since most undergraduate texts do not cover this material or do so in a cursory way. The result is a clear, concise, well-organized introduction to such topics as the Riemann integral, measurable sets, properties of measurable sets, measurable functions, the Lebesgue integral, convergence and the Lebesgue integral, pointwise convergence of Fourier series and other subjects. The authors not only cover these topics in a useful and thorough way, they have taken pains to motivate the student by keeping the goals of the theory always in sight, justifying each step of the development in terms of those goals. In addition, whenever possible, new concepts are related to concepts already in the student's repertoire. Finally, to enable readers to test their grasp of the material, the text is supplemented by numerous examples and exercises. Mathematics students as well as students of engineering and science will find here a superb treatment, carefully thought out and well presented , that is ideal for a one semester course. The only prerequisite is a basic knowledge of advanced calculus, including the notions of compactness, continuity, uniform convergence and Riemann integration.