Mathematical methods in physics. Distributions, Hilbert space operators, and variational methods
type: Item
instance of: scholarly article
title: Mathematical methods in physics. Distributions, Hilbert space operators, and variational methods
zbMATH Open document ID: 1019.46001
author: Ph. Blanchard
author: E. Brüning
published in: Progress in Mathematical Physics
publication date: 2003-01-06T00:00:00Z
review text: The text is a translated version of a book originally published in German by Springer in 1993. So the previous review in Zbl 0799.46001 still applies. Yet the 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. Still, like the German version, the present text focusses on and restricts to three vital strands of contemporary mathematical physics: distribution theory, operators in Hilbert space, and variational methods. 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. In principle, the book is self-contained, the only prerequisites being a solid background in analysis and linear algebra.
Mathematics Subject Classification ID: 46-01
Mathematics Subject Classification ID: 47-01
Mathematics Subject Classification ID: 46F05
Mathematics Subject Classification ID: 46F10
Mathematics Subject Classification ID: 46F12
Mathematics Subject Classification ID: 47A10
Mathematics Subject Classification ID: 47B25
Mathematics Subject Classification ID: 47A75
zbMATH DE Number: 1849085
zbMATH Keywords: spaces of generalized functions
zbMATH Keywords: hypoelliptic differential operators
zbMATH Keywords: distribution theory
zbMATH Keywords: operators in Hilbert space
zbMATH Keywords: variational methods
reviewed by: Gert Roepstorff
MaRDI profile type: Publication
Recommended article: Mathematical methods in physics. Distributions, Hilbert space operators, variational methods, and applications in quantum physics
Recommended article: Q3996220
Recommended article: Analysis.
Recommended article: Q4285466
Recommended article: Exercises and problems in mathematical methods of physics
Recommended article: Q4382680
Recommended article: Q4715453
Recommended article: Mathematics for physicists
Recommended article: Q3490496
Recommended article: Q3525135
description: scientific article; zbMATH DE number 1849085