Spectral estimates for two-dimensional Schrödinger operators with application to quantum layers

DOI10.1007/s00220-007-0318-zzbMath1140.81385arXivmath-ph/0612070OpenAlexW2137767067MaRDI QIDQ930562

Timo Weidl, Hynek Kovařík, Semjon A. Vugalter

Publication date: 1 July 2008

Published in: Communications in Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math-ph/0612070

Mathematics Subject Classification ID

Estimates of eigenvalues in context of PDEs (35P15) Selfadjoint operator theory in quantum theory, including spectral analysis (81Q10) Schrödinger operator, Schrödinger equation (35J10)

Related Items (5)

The Lieb–Thirring inequalities: Recent results and open problems ⋮ Eigenvalue bounds for two-dimensional magnetic Schrödinger operators ⋮ Estimates on trapped modes in deformed quantum layers ⋮ Eigenvalue bounds for perturbations of Schrödinger operators and Jacobi matrices with regular ground states ⋮ A simple proof of Hardy-Lieb-Thirring inequalities

Cites Work

• Lieb-Thirring inequalities on the half-line with critical exponent
• The bound state of weakly coupled Schrödinger operators in one and two dimensions
• Weak type estimates for singular values and the number of bound states of Schrödinger operators
• Piecewise-polynomial approximation of functions from \(H^ \ell((0,1)^ d)\), \(2\ell=d\), and applications to the spectral theory of the Schrödinger operator
• On the Lieb-Thirring constants \(L_{\gamma, 1}\) for \(\gamma \geq 1/2\)
• Bounds on the eigenvalues of the Laplace and Schroedinger operators
• An estimate for the number of bound states of the Schrödinger operator in two dimensions
• Bound states in one and two spatial dimensions
• [https://portal.mardi4nfdi.de/wiki/Publication:4893803 The negative discrete spectrum of a two-dimensional Schr�dinger operator]
• The negative spectrum of a class of two-dimensional Schrödinger operators with potentials depending only on radius
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item

This page was built for publication: Spectral estimates for two-dimensional Schrödinger operators with application to quantum layers