Schrödinger Operators: Eigenvalues and Lieb-Thirring Inequalities

ISBN-13: 9781009218467 / Angielski / Twarda / 2022 / 512 str.

Timo (Universitat Stuttgart) Weidl

Opis

Takes readers from the very basic facts to the most recent results on eigenvalues of Laplace and Schrödinger operators.

Recenzje

'In a difficult 1968 paper Dyson and Lenard succeeded in proving the 'Stability of Matter' in quantum mechanics. In 1975 a much simpler proof was developed by Thirring and me with a new, multi-function, Sobolev like inequality, as well as a bound on the negative spectrum of Schrödinger operators. These and other bounds have become an important and useful branch of functional analysis and differential equations generally and quantum mechanics in particular. This book, written by three of the leading contributors to the area, carefully lays out the entire subject in a highly readable, yet complete description of these inequalities. They also give gently, yet thoroughly, all the necessary spectral theory and Sobolev theory background that a beginning student might need.' Elliott Lieb, Princeton University

Spis treści

Overview; Part I. Background Material: 1. Elements of operator theory; 2. Elements of Sobolev space theory; Part II. The Laplace and Schrödinger Operators: 3. The Laplacian on a domain; 4. The Schrödinger operator; Part III. Sharp Constants in Lieb–Thirring Inequalities:5. Sharp Lieb–Thirring inequalities; 6. Sharp Lieb–Thirring inequalities in higher dimensions; 7. More on sharp Lieb–Thirring inequalities; 8. More on the Lieb–Thirring constants; References; Index.