Schroedinger Operator with Strong Magnetic Field near Boundary
Abstract
We consider 2dimensional Schroedinger operator with the nondegenerating magnetic field in the domain with the boundary and under certain nondegeneracy assumptions we derive spectral asymptotics with the remainder estimate better than $O(h^{1})$, up to $O(\mu^{1}h^{1})$ and the principal part $\asymp h^{2}$ where $h\ll 1$ is Planck constant and $\mu \gg 1$ is the intensity of the magnetic field; $\mu h \le 1$. We also consider generalized SchrödingerPauli operator in the same framework albeit with $\mu h\ge 1$ and derive spectral asymptotics with the remainder estimate up to O(1) and with the principal part $\asymp \mu h^{1}$, or, under certain special circumstances with the principal part $\asymp \mu^{1/2} h^{1/2}$.
 Publication:

arXiv eprints
 Pub Date:
 May 2010
 arXiv:
 arXiv:1005.0244
 Bibcode:
 2010arXiv1005.0244I
 Keywords:

 Mathematics  Spectral Theory;
 Mathematical Physics;
 Mathematics  Analysis of PDEs;
 35P20
 EPrint:
 100 pp, 34 fig