Unitary reduction for the two-dimensional Schrödinger operator with strong magnetic field

2007 ◽  
Vol 344 (11) ◽  
pp. 715-719
Author(s):  
Andrei Eckstein
Keyword(s):  
Magnetic Field ◽  
Strong Magnetic Field ◽  
Schrödinger Operator ◽  
Two Dimensional ◽  
Schrodinger Operator

Eigenvalues and eigenfunctions for the two dimensional Schrödinger operator with strong magnetic field

2020 ◽  
Vol 120 (1-2) ◽  
pp. 175-197
Author(s):  
Naoya Yoshida
Keyword(s):  
Magnetic Field ◽  
Schrödinger Operator ◽  
Scalar Potential ◽  
Energy Curve ◽  
Effective Hamiltonian ◽  
Two Dimensional ◽  
Schrodinger Operator ◽  
Eigenvalues And Eigenfunctions ◽  
Pseudodifferential Calculus ◽  
Distribution Of Eigenvalues

We study the eigenvalues of the two-dimensional Schrödinger operator with a large constant magnetic field perturbed by a decaying scalar potential. For each Landau level, we give the precise asymptotic distribution of eigenvalues created by the minimum, maximum and the closed energy curve of the potential. Normal form reduction, WKB construction and pseudodifferential calculus are applied to the effective Hamiltonian.

scholarly journals On the two-dimensional Schrödinger operator with an attractive potential of the Bessel-Macdonald type

2020 ◽  
pp. 168385
Author(s):  
Wellisson B. De Lima ◽  
Oswaldo M. Del Cima ◽  
Daniel H.T. Franco ◽  
Bruno C. Neves
Keyword(s):  
Schrödinger Operator ◽  
Attractive Potential ◽  
Two Dimensional ◽  
Schrodinger Operator
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