On the Schrödinger operator with periodic point interactions in the three‐dimensional case

1984 ◽  
Vol 25 (10) ◽  
pp. 2910-2917 ◽  
Author(s):  
S. Fassari
Keyword(s):  
Periodic Point ◽  
Schrödinger Operator ◽  
Three Dimensional ◽  
Dimensional Case ◽  
Schrodinger Operator ◽  
Point Interactions

NORM RESOLVENT CONVERGENCE TO MAGNETIC SCHRÖDINGER OPERATORS WITH POINT INTERACTIONS

2001 ◽  
Vol 13 (04) ◽  
pp. 465-511 ◽  
Author(s):  
HIDEO TAMURA
Keyword(s):  
Magnetic Field ◽  
Boundary Conditions ◽  
Schrödinger Operator ◽  
Schrödinger Operators ◽  
Two Dimensions ◽  
Schrodinger Operators ◽  
Schrodinger Operator ◽  
Point Interactions ◽  
Resolvent Convergence ◽  
Norm Resolvent Convergence

The Schrödinger operator with δ-like magnetic field at the origin in two dimensions is not essentially self-adjoint. It has the deficiency indices (2, 2) and each self-adjoint extension is realized as a differential operator with some boundary conditions at the origin. We here consider Schrödinger operators with magnetic fields of small support and study the norm resolvent convergence to Schrödinger operator with δ-like magnetic field. We are concerned with the boundary conditions realized in the limit when the support shrinks. The results obtained heavily depend on the total flux of magnetic field and on the resonance space at zero energy, and the proof is based on the analysis at low energy for resolvents of Schrödinger operators with magnetic potentials slowly falling off at infinity.

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