scholarly journals Eigenvalue bounds for two-dimensional magnetic Schrödinger operators

2011 ◽  
pp. 363-387 ◽  
Author(s):  
Hynek Kovařík
Keyword(s):  
Schrödinger Operators ◽  
Schrodinger Operators ◽  
Two Dimensional ◽  
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 Heat Kernel Coefficients for Two-Dimensional Schrödinger Operators

2008 ◽  
Vol 283 (3) ◽  
pp. 853-860 ◽  
Author(s):  
Yuri Berest ◽  
Tim Cramer ◽  
Farkhod Eshmatov
Keyword(s):  
Heat Kernel ◽  
Schrödinger Operators ◽  
Schrodinger Operators ◽  
Two Dimensional

scholarly journals Two-Dimensional Periodic Schrödinger Operators Integrable at an Energy Eigenlevel

2019 ◽  
Vol 53 (1) ◽  
pp. 23-36
Author(s):  
A. V. Ilina ◽  
I. M. Krichever ◽  
N. A. Nekrasov
Keyword(s):  
Schrödinger Operators ◽  
Schrodinger Operators ◽  
Two Dimensional
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