Mathematical methods in physics. Distributions, Hilbert space operators, and variational methods
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.
scientific article; zbMATH DE number 1849085