Blanchard / Bruening Mathematical Methods in Physics

Distributions, Hilbert Space Operators, and Variational Methods
Erscheinungsjahr 2012
ISBN: 978-1-4612-0049-9
Verlag: Birkhäuser Boston
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, Band 26, 471 Seiten, eBook

Reihe: Progress in Mathematical Physics

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.

Zielgruppe

Research

Autoren/Hrsg.

Blanchard, Philippe

Bruening, Erwin

Inhaltsverzeichnis

I Distributions.- 1 Introduction.- 2 Spaces of Test Functions.- 3 Schwartz Distributions.- 4 Calculus for Distributions.- 5 Distributions as Derivatives of Functions.- 6 Tensor Products.- 7 Convolution Products.- 8 Applications of Convolution.- 9 Holomorphic Functions.- 10 Fourier Transformation.- 11 Distributions and Analytic Functions.- 12 Other Spaces of Generalized Functions.- II Hilbert Space Operators.- 13 Hiilbert Spaces: A Brief Historical Introduction.- 14 Inner Product Spaces and Hilbert Spaces.- 15 Geometry of Hilbert Spaces.- 16 Separable Hilbert Spaces.- 17 Direct Sums and Tensor Products.- 18 Topological Aspects.- 19 Linear Operators.- 20 Quadratic Forms.- 21 Bounded Linear Operators.- 22 Special Classes of Bounded Operators.- 23 Self-adjoint Hamilton Operators.- 24 Elements of Spectral Theory.- 25 Spectral Theory of Compact Operators.- 26 The Spectral Theorem.- 27 Some Applications of the Spectral Representation.- III Variational Methods.- 28 Introduction.- 29 Direct Methods in the Calculus of Variations.- 30 Differential Calculus on Banach Spaces and Extrema of Functions.- 31 Constrained Minimization Problems (Method of Lagrange Multipliers).- 32 Boundary and Eigenvalue Problems.- 33 Density Functional Theory of Atoms and Molecules.- IV Appendix.- A Completion of Metric Spaces.- B Metrizable Locally Convex Topological Vector Spaces.- C The Theorem of Baire.- C.1 The uniform boundedness principle.- C.2 The open mapping theorem.- D Bilinear Functionals.- References.