Schroedinger Operator with Strong Magnetic Field near Boundary

Abstract: We consider 2-dimensional Schroedinger operator with the non-degenerating magnetic field in the domain with the boundary and under certain non-degeneracy assumptions we derive spectral asymptotics with the remainder estimate better than

O (h^{- 1})

, up to

O (m u^{- 1} h^{- 1})

and the principal part

a s y m p h^{- 2}

where

h l l 1

is Planck constant and

m u g g 1

is the intensity of the magnetic field;

m u h l e 1

. We also consider generalized Schr"odinger-Pauli operator in the same framework albeit with

m u h g e 1

and derive spectral asymptotics with the remainder estimate up to O(1) and with the principal part

a s y m p m u h^{- 1}

, or, under certain special circumstances with the principal part

a s y m p m u^{1 / 2} h^{- 1 / 2}

.

Mathematics Subject Classification ID

Asymptotic distributions of eigenvalues in context of PDEs (35P20)

This page was built for publication: Schroedinger Operator with Strong Magnetic Field near Boundary

Report a bug (only for logged in users!)Click here to report a bug for this page (MaRDI item Q6502734)