Mathematical Methods in Physics : Distributions, Hilbert Space Operators, and Variational Methods

Brüning, Erwin, Blanchard, Philippe

ISBN 10: 0817642285 / ISBN 13: 9780817642280

Published by Birkhäuser Boston, 2002

About this Item

Former library book; may include library markings. Used book that is in excellent condition. May show signs of wear or have minor defects.

Seller Inventory # GRP21266010

Bibliographic Details

• Title: Mathematical Methods in Physics : Distributions, Hilbert Space Operators, and Variational Methods
• Publisher: Birkhäuser Boston
• Publication Date: 2002
• Language: English
• ISBN 10: 0817642285
• ISBN 13: 9780817642280
• Binding: Hardcover
• Condition: Very Good

About this title

Synopsis

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.

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.