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 …

This monograph offers a state-of-the-art mathematical account of functional integration
methods in the context of self-adjoint operators and semigroups using the concepts and …

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 …

arXiv:math-ph/0510055v2 2 Nov 2005 Recent developments in quantum mechanics with
magnetic fields Page 1 arXiv:math-ph/0510055v2 2 Nov 2005 Recent developments in …

Let A be a self-adjoint operator acting over a space X endowed with a partition. We give
lower bounds on the energy of a mixed state ρ from its distribution in the partition and the …

We consider the eigenvalues of the magnetic Laplacian on a bounded domain Ω of R 2 with
uniform magnetic field β> 0 and magnetic Neumann boundary conditions. We find upper …

We consider the magnetic Dirichlet Laplacian with constant magnetic field on domains of
finite measure. First, in the case of a disk, we prove that the eigenvalue branches with …

We give an improvement of sharp Berezin type bounds on the Riesz means $\sum_k
(\Lambda-\lambda_k) _+^\sigma $ of the eigenvalues $\lambda_k $ of the Dirichlet …

Abstract We consider the Dirichlet Laplacian with a constant magnetic field in a two-
dimensional domain of finite measure. We determine the sharp constants in semi-classical …

We prove various estimates for the first eigenvalue of the magnetic Dirichlet Laplacian on a
bounded, open, simply connected domain in two dimensions. When the magnetic field is …