Schrödinger Operators: Eigenvalues and Lieb–Thirring Inequalities

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Schrödinger Operators: Eigenvalues and Lieb–Thirring Inequalities is written by Rupert L. Frank and published by Cambridge University Press. It's available with International Standard Book Number or ISBN identification 1009218441 (ISBN 10) and 9781009218443 (ISBN 13).

The analysis of eigenvalues of Laplace and Schrödinger operators is an important and classical topic in mathematical physics with many applications. This book presents a thorough introduction to the area, suitable for masters and graduate students, and includes an ample amount of background material on the spectral theory of linear operators in Hilbert spaces and on Sobolev space theory. Of particular interest is a family of inequalities by Lieb and Thirring on eigenvalues of Schrödinger operators, which they used in their proof of stability of matter. The final part of this book is devoted to the active research on sharp constants in these inequalities and contains state-of-the-art results, serving as a reference for experts and as a starting point for further research.