scholarly journals Eigenvalue Bounds for Perturbations of Schrödinger Operators and Jacobi Matrices With Regular Ground States

2008 ◽  
Vol 282 (1) ◽  
pp. 199-208 ◽  
Author(s):  
Rupert L. Frank ◽  
Barry Simon ◽  
Timo Weidl
Keyword(s):  
Schrödinger Operators ◽  
Ground States ◽  
Jacobi Matrices ◽  
Schrodinger Operators ◽  
Eigenvalue Bounds

scholarly journals Eigenvalue bounds in the gaps of Schrödinger operators and Jacobi matrices

2008 ◽  
Vol 340 (2) ◽  
pp. 892-900 ◽  
Author(s):  
Dirk Hundertmark ◽  
Barry Simon
Keyword(s):  
Schrödinger Operators ◽  
Jacobi Matrices ◽  
Schrodinger Operators ◽  
Eigenvalue Bounds

scholarly journals Eigenvalue Bounds for Schrödinger Operators with a Homogeneous Magnetic Field

2011 ◽  
Vol 97 (3) ◽  
pp. 227-241 ◽  
Author(s):  
Rupert L. Frank ◽  
Rikard Olofsson
Keyword(s):  
Magnetic Field ◽  
Schrödinger Operators ◽  
Homogeneous Magnetic Field ◽  
Schrodinger Operators ◽  
Eigenvalue Bounds

scholarly journals Spectral Analysis of Schrödinger Operators with Unusual Semiclassical Behavior

10.14311/1801 ◽  
2013 ◽  
Vol 53 (3) ◽  
Author(s):  
Pavel Exner ◽  
Diana Barseghyan
Keyword(s):  
Spectral Analysis ◽  
Phase Space ◽  
Lower Bounds ◽  
Dirichlet Boundary ◽  
Schrödinger Operators ◽  
Critical Value ◽  
Upper And Lower Bounds ◽  
Schrodinger Operators ◽  
Two Dimensional ◽  
Eigenvalue Bounds

In this paper we discuss several examples of Schrödinger operators describing a particle confined to a region with thin cusp-shaped ‘channels’, given either by a potential or by a Dirichlet boundary; we focus on cases when the allowed phase space is infinite but the operator still has a discrete spectrum. First we analyze two-dimensional operators with the potential |xy|p - ?(x2 + y2)p/(p+2)where p?1 and ??0. We show that there is a critical value of ? such that the spectrum for ??crit it is unbounded from below. In the subcriticalcase we prove upper and lower bounds for the eigenvalue sums. The second part of work is devoted toestimates of eigenvalue moments for Dirichlet Laplacians and Schrödinger operators in regions havinginfinite cusps which are geometrically nontrivial being either curved or twisted; we are going to showhow these geometric properties enter the eigenvalue bounds.

scholarly journals Bound states and the Szegő condition for Jacobi matrices and Schrödinger operators

2003 ◽  
Vol 205 (2) ◽  
pp. 357-379 ◽  
Author(s):  
David Damanik ◽  
Dirk Hundertmark ◽  
Barry Simon
Keyword(s):  
Bound States ◽  
Schrödinger Operators ◽  
Jacobi Matrices ◽  
Schrodinger Operators

scholarly journals Eigenvalue Bounds for a Class of Schrödinger Operators in a Strip

2018 ◽  
Vol 2018 ◽  
pp. 1-8 ◽  
Author(s):  
Martin Karuhanga
Keyword(s):  
Boundary Conditions ◽  
Bound States ◽  
Schrödinger Operators ◽  
Neumann Boundary ◽  
Neumann Boundary Conditions ◽  
Schrodinger Operators ◽  
Eigenvalue Bounds ◽  
Negative Eigenvalues

This paper is concerned with the estimation of the number of negative eigenvalues (bound states) of Schrödinger operators in a strip subject to Neumann boundary conditions. The estimates involve weighted L1 norms and Lln⁡L norms of the potential. Estimates involving the norms of the potential supported by a curve embedded in a strip are also presented.

Sign in / Sign up

Export Citation Format

Share Document