Quantenmechanik und Mathematik (English shop)

Teil 1: Normierte Räume, Spektraltheorie

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Preface, PDF (38 KB)
Extract, PDF (180 KB)
Table of Contents, PDF (49 KB)

This work describes, in two volumes, that part of mathematics from which non-relativistic quantum mechanics in the Hilbert space formulation is constructed. This is done from a purely technical point of view in the sense of mathematical physics, yet not under the constraints of physical usefulness and applicability, but rather under those of engaging with mathematics for its own sake. The central questions are therefore: What interesting facts does the mathematics of quantum mechanics have to offer? What connections exist between its individual areas? What generalisations are known, and what happens if one mathematically transgresses physically motivated restrictions? The first volume focuses, alongside topological as well as measure- and integration-theoretic foundations, on Banach spaces and Hilbert spaces and, in particular, on the spectral theory of bounded and unbounded operators. In doing so, the book leads, among other things, into areas of functional analysis that go considerably beyond the topics treated in standard textbooks and that in part can so far be found only in the original literature.