[图书][B] Schrödinger operators: eigenvalues and Lieb–Thirring inequalities
RL Frank, A Laptev, T Weidl - 2022 - books.google.com
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 …
classical topic in mathematical physics with many applications. This book presents a …
[PDF][PDF] The Lieb-Thirring inequalities: recent results and open problems
RL Frank - arXiv preprint arXiv:2007.09326, 2020 - arxiv.org
arXiv:2007.09326v1 [math-ph] 18 Jul 2020 Page 1 arXiv:2007.09326v1 [math-ph] 18 Jul 2020
THE LIEB–THIRRING INEQUALITIES: RECENT RESULTS AND OPEN PROBLEMS RUPERT …
THE LIEB–THIRRING INEQUALITIES: RECENT RESULTS AND OPEN PROBLEMS RUPERT …
Universal functionals in density functional theory
In this chapter we first review the Levy–Lieb functional, which gives the lowest kinetic and
interaction energy that can be reached with all possible quantum states having a given …
interaction energy that can be reached with all possible quantum states having a given …
Lieb–Thirring inequalities with improved constants
A Laptev, J Dolbeault, M Loss - Journal of the European Mathematical …, 2008 - ems.press
Abstract Following Eden and Foias we obtain a matrix version of a generalised Sobolev
inequality in one-dimension. This allows us to improve on the known estimates of best …
inequality in one-dimension. This allows us to improve on the known estimates of best …
The Lieb–Thirring inequality revisited
The Lieb–Thirring inequality revisited Page 1 © 2021 European Mathematical Society
Published by EMS Press. This work is licensed under a CC BY 4.0 license. J. Eur. Math. Soc …
Published by EMS Press. This work is licensed under a CC BY 4.0 license. J. Eur. Math. Soc …
Green's function asymptotics and sharp interpolation inequalities
SV Zelik, AA Ilyin - Russian Mathematical Surveys, 2014 - iopscience.iop.org
A general method is proposed for finding sharp constants for the embeddings of the Sobolev
spaces $ H^ m (\mathscr {M}) $ on an $ n $-dimensional Riemannian manifold $\mathscr {M} …
spaces $ H^ m (\mathscr {M}) $ on an $ n $-dimensional Riemannian manifold $\mathscr {M} …
Lieb–Thirring type inequalities and Gagliardo–Nirenberg inequalities for systems
This paper is devoted to inequalities of Lieb–Thirring type. Let V be a nonnegative potential
such that the corresponding Schrödinger operator has an unbounded sequence of …
such that the corresponding Schrödinger operator has an unbounded sequence of …
Some bound state problems in quantum mechanics
D Hundertmark - Proceedings of Symposia in Pure Mathematics, 2007 - books.google.com
We give a review of semi-classical estimates for bound states and their eigenvalues for
Schrödinger operators. Motivated by the classical results, we discuss their recent …
Schrödinger operators. Motivated by the classical results, we discuss their recent …
The state of the Lieb--Thirring conjecture
L Schimmer - arXiv preprint arXiv:2203.06051, 2022 - arxiv.org
In 1976 Lieb and Thirring established upper bounds on sums of powers of the negative
eigenvalues of a Schr\" odinger operator in terms of semiclassical phase-space integrals …
eigenvalues of a Schr\" odinger operator in terms of semiclassical phase-space integrals …
[PDF][PDF] Spectral inequalities for partial differential equations and their applications
A Laptev - AMS/IP Stud. Adv. Math, 2012 - wwwf.imperial.ac.uk
(1.1) H=−∆+ V, where V is a real-valued function. If the potential function V decays rapidly
enough and, for example, smooth, then the spectrum of the operator H typically is absolutely …
enough and, for example, smooth, then the spectrum of the operator H typically is absolutely …