Schroedinger Operator with Strong Magnetic Field near Boundary
Victor Yakovlevich Ivrii · arXiv (Cornell University) · 2010
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 $O(μ^{-1}h^{-1})$ and the principal part $\asymp h^{-2}$ where $h\ll 1$ is Planck constant and $μ\gg 1$ is the intensity of the magnetic field; $μh \le 1$. We also consider generalized Schrödinger-Pauli operator in the same framework albeit with $μh\ge 1$ and derive spectral asymptotics with the remainder estimate up to O(1) and with the principal part $\asymp μh^{-1}$, or, under certain special circumstances with the principal part $\asymp μ^{1/2} h^{-1/2}$.