Philippe Blanchard, Erwin Bruening

Mathematical Methods in Physics (eBook, PDF)

Distributions, Hilbert Space Operators, and Variational Methods

• Format: PDF

Produktbeschreibung

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.

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Produktdetails

• Verlag: Birkhäuser Boston
• Seitenzahl: 471
• Erscheinungstermin: 6. Dezember 2012
• Englisch
• ISBN-13: 9781461200499
• Artikelnr.: 44194642

Autorenporträt

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.

Inhaltsangabe

Introduction.- Spaces of Test Functions.- Schwartz Distributions.- Calculus for Distributions.- Distributions as Derivatives of Functions.- Tensor Products.- Convolution Products.- Applications of Convolution.- Holomorphic Functions.- Fourier Transformations.- Distributions as Boundary Values of Analytic Functions.- Other Spaces of Generalized Functions.- Sobolev Spaces.- Hilbert Spaces: A Brief Historical Introduction.- Inner Product Spaces and Hilbert Spaces.- Geometry of Hilbert Spaces.- Separable Hilbert Spaces.- Direct Sums and Tensor Products.- Topological Aspects.- Linear Operators.- Quadratic Forms.- Bounded Linear Operators.- Special Classes of Linear Operators.- Elements of Spectral Theory.- Compact Operators.- Hilbert-Schmidt and Trace Class Operators.- The Spectral Theorem.- Some Applications of the Spectral Representation.- Spectral Analysis in Rigged Hilbert Spaces.- Operator Algebras and Positive Mappings.- Positive Mappings in Quantum Physics.- Introduction.- DirectMethods in the Calculus of Variations.- Differential Calculus on Banach Spaces and Extrema of Functions.- Constrained Minimization Problems (Method of Lagrange Multipliers).- Boundary and Eigenvalue Problems.- Density Functional Theory of Atoms and Molecules.- Appendices.- Index.

Rezensionen

"This book gives a detailed survey on mathematical methods in physics ... . The book is very suitable for students of physics, mathematics or engineering with a good background in analysis and linear algebra. ... All in all, the book has a high didactical and scientific quality so that it can be recommended for both graduate students and researchers." (Michael Demuth, zbMATH 1330.46001, 2016)