scholarly journals Weyl formulae for Schrödinger operators with critically singular potentials

2021 ◽  
pp. 1-46
Author(s):  
Xiaoqi Huang ◽  
Christopher D. Sogge
Keyword(s):  
Schrödinger Operators ◽  
Schrodinger Operators ◽  
Singular Potentials

scholarly journals Commutation methods for Schrödinger operators with strongly singular potentials

2011 ◽  
Vol 285 (4) ◽  
pp. 392-410 ◽  
Author(s):  
Aleksey Kostenko ◽  
Alexander Sakhnovich ◽  
Gerald Teschl
Keyword(s):  
Schrödinger Operators ◽  
Schrodinger Operators ◽  
Singular Potentials ◽  
Strongly Singular Potentials

Mild singular potentials as effective Laplacians in narrow strips

2017 ◽  
Vol 120 (1) ◽  
pp. 145
Author(s):  
César R. De Oliveira ◽  
Alessandra A. Verri
Keyword(s):  
Boundary Conditions ◽  
Quadratic Forms ◽  
Dirichlet Boundary ◽  
Schrödinger Operators ◽  
Dirichlet Boundary Conditions ◽  
Schrodinger Operators ◽  
Singular Potentials ◽  
One Dimensional ◽  
Effective Operators

We propose to obtain information on one-dimensional Schrödinger operators on bounded intervals by approaching them as effective operators of the Laplacian in thin planar strips.  Here we develop this idea to get spectral knowledge of some mild singular potentials with Dirichlet boundary conditions.  Special preparations, including a result on perturbations of quadratic forms, are included as well.

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