Schroedinger Operators: Eigenvalues and Lieb-Thirring Inequalities

The analysis of eigenvalues of Laplace and Schrödinger operators is a fundamental topic in mathematical physics, with applications in various fields. This book provides a comprehensive introduction to the area, suitable for advanced students and researchers, and covers background material on spectral theory and Sobolev space theory. It also discusses a family of inequalities by Lieb and Thirring on Schrödinger operators, which are used to prove stability of matter. The final part of the book focuses on recent research on sharp constants in these inequalities, offering state-of-the-art results and serving as a reference for experts and a starting point for further research.

Format: Hardback
Length: 512 pages
Publication date: 17 November 2022
Publisher: Cambridge University Press

The study of the eigenvalues of Laplace and Schrödinger operators is a fundamental and renowned topic in mathematical physics, boasting numerous practical applications. This comprehensive book offers a thorough introduction to this field, catering to both masters and graduate students. It provides ample background material on the spectral theory of linear operators in Hilbert spaces and Sobolev space theory, making it an ideal resource for those seeking to delve into this domain.

One of the key aspects of this book is its exploration of a family of inequalities by Lieb and Thirring, which play a crucial role in proving the stability of matter. These inequalities concern the eigenvalues of Schrödinger operators and have profound implications for understanding the behavior of physical systems. The final section of the book is dedicated to ongoing research on sharp constants in these inequalities, presenting state-of-the-art results that serve as a valuable reference for experts and a fertile ground for future research endeavors.

In summary, this book provides a comprehensive and accessible introduction to the analysis of eigenvalues of Laplace and Schrödinger operators, making it an essential resource for students and scholars in the field of mathematical physics. Its focus on inequalities and their applications to stability theory sets it apart from other texts, making it a valuable addition to any academic library.

Weight: 918g
Dimension: 159 x 236 x 41 (mm)
ISBN-13: 9781009218467