Mathematical Methods in Physics: Distributions, Hilbert Space Operators, and Variational Methods (Progress in Mathematical Physics, 26, Band 26) - Hardcover

Blanchard, Philippe; Bruening, Erwin

Hardcover

ISBN 10: 0817642285 ISBN 13: 9780817642280

Verlag: Birkhäuser, 2002

Inhaltsangabe

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.

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Über die Autorin bzw. den Autor

Johannes Angermüller is Professor in the School of Languages and Applied Linguistics at the Open University, UK. Philippe Blanchard is Associate Professor in the Department of Politics and International Studies at the University of Warwick, UK.

Von der hinteren Coverseite

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.

Details zur Ausgabe

• Verlag: Birkhäuser
• Erscheinungsdatum: 2002
• Sprache: Englisch
• ISBN 10: 0817642285
• ISBN 13: 9780817642280
• Einband: Gebundene Ausgabe
• Anzahl der Seiten: 494
• Kontakt zum Hersteller: Springer Nature Customer Service Center GmbH; ProductSafety@springernature.com; ; Europaplatz 3; Heidelberg; 69115; Deutschland