Ebook Mathematical Methods in Physics: Distributions, Hilbert Space Operators, and Variational Methods (Progress in Mathematical Physics, Vol. 26
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Mathematical Methods in Physics: Distributions, Hilbert Space Operators, and Variational Methods (Progress in Mathematical Physics, Vol. 26
Ebook Mathematical Methods in Physics: Distributions, Hilbert Space Operators, and Variational Methods (Progress in Mathematical Physics, Vol. 26
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Physics has long been regarded as a wellspring of mathematical problems. Mathematical Methods in Physics is a self-contained presentation, driven by historic motivations, excellent examples, detailed proofs, and a focus on those parts of mathematics that are needed in more ambitious courses on quantum mechanics and classical and quantum field theory. Aimed primarily at a broad community of graduate students in mathematics, mathematical physics, physics and engineering, as well as researchers in these disciplines.
- Sales Rank: #1864050 in Books
- Published on: 2002-10-04
- Original language: English
- Number of items: 1
- Dimensions: 9.21" h x 1.00" w x 6.14" l, 1.88 pounds
- Binding: Hardcover
- 471 pages
Review
"This text is a translated, considerably revised and extended version of the book Distributionen und Hilbertraumoperatoren: Mathematische Methoden der Physik.... The book is written in a very nice and understandable form and addresses mainly students with interest in the interaction between physics and mathematics."
―Mathematica Bohemica
". . . [This] English version has been considerably revised and extended in order to improve the usefulness for students of physics and mathematics alike. For instance, proofs are now more detailed. Many added examples illustrate abstract mathematical concepts. Exercises were included to improve the skill of beginners. Some of these exercises hint to physical problems arising either in quantum mechanics or field theory. . . . Notably, there is one chapter at the end, dealing exclusively with physics applications, the density functional theory of atoms and molecules due to Hohenberg, Kohn, and Sham. In my view this is a nice way to illustrate the calculus of variations. . . . the book is self-contained, the only prerequisites being a solid background in analysis and linear algebra."
―Zentralblatt Math
"...many very nice and useful examples and applications are provided." ---Monatshefte für Mathematik
From the Back Cover
Physics has long been regarded as a wellspring of mathematical problems. Mathematical Methods in Physics is a self-contained presentation, driven by historic motivations, excellent examples, detailed proofs, and a focus on those parts of mathematics that are needed in more ambitious courses on quantum mechanics and classical and quantum field theory. A comprehensive bibliography and index round out the work.
Key Topics: Part I: A brief introduction to (Schwartz) distribution theory; Elements from the theories of ultra distributions and hyperfunctions are given in addition to some deeper results for Schwartz distributions, thus providing a rather comprehensive introduction to the theory of generalized functions. Basic properties of and basic properties for distributions are developed with applications to constant coefficient ODEs and PDEs; the relation between distributions and holomorphic functions is developed as well. * Part II: Fundamental facts about Hilbert spaces and their geometry. The theory of linear (bounded and unbounded) operators is developed, focusing on results needed for the theory of Schr"dinger operators. The spectral theory for self-adjoint operators is given in some detail. * Part III: Treats the direct methods of the calculus of variations and their applications to boundary- and eigenvalue-problems for linear and nonlinear partial differential operators, concludes with a discussion of the Hohenberg--Kohn variational principle. * Appendices: Proofs of more general and deeper results, including completions, metrizable Hausdorff locally convex topological vector spaces, Baire's theorem and its main consequences, bilinear functionals.
Aimed primarily at a broad community of graduate students in mathematics, mathematical physics, physics and engineering, as well as researchers in these disciplines.
About the Author
Philippe Blanchard is Professor of Mathematical Physics at Bielefeld University in Germany. Erwin Bruening is a Research Fellow at the University of KwaZulu-Natal in South Africa.
Most helpful customer reviews
6 of 6 people found the following review helpful.
A Fantastic Romp
By Joshu
Blanchard's text is an excelent journey through a variety of topics in mathematical physics. The language is clearly more closely related to an advanced physics text than a math text, and Blanchard strives to give explanations as well as just rigorous proofs to accompany his results. It makes for a truly interesting read where one can gain essential details without having to necessarily be weighed down by long proofs (which are usually set in a smaller font so as to allow one to skip them at will).
The choice of exercises is likewise superb, ranging from the trivial to the truly difficult. It is not, however, too uncommon to find that one needs more knoweldge than can be found in the text to really complete a problem. Students of this text would be better suited adding at least two courses in real analysis to Blanchard's suggested list.
Still, the selection of important topics to cover is great, the examples chosen are lucid, and the exposition is memorable. I highly recommend this book to anyone looking for an interesting read, who is unfamiliar with distributions or hilbert space operators in particular.
0 of 2 people found the following review helpful.
Five Stars
By Constantine K.
As expected.
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