Related papers: Schroedinger Operator with Strong Magnetic Field n…
We consider 2-dimensional Schr\"odinger operator with the non-degenerating magnetic field and we discuss spectral asymptotics with the remainder estimate $o(\mu^{-1}h^{-1})$ or better. We also consider 3-dimensional Schr\"odinger operator…
I consider 4-dimensional Schr\"odinger operator with the generic non-degenerating magnetic field and for a generic potential I derive spectral asymptotics with the remainder estimate $O(\mu^{-1}h^{-3})$ and the principal part $\asymp…
I consider two-dimensional Schr\"odinger operator with degenerating magnetic field and in the generic situation I derive spectral asymptotics as $h\to +0$ and $\mu\to +\infty$ where $h$ and $\mu$ are Planck and coupling parameters…
I continue analysis of the Schr\"odinger operator with the strong degenerating magnetic field, started in \cite{IRO6}. Now I consider 4-dimensional case, assuming that magnetic field is generic degenerated and under certain conditions I…
With derive sharp spectral asymptotics (with the remainder estimate $O(\mu ^{-1}h^{1-d}+\mu ^{\frac{d} {2}-1}h^{1-\frac{d}{2}})$ for $d$-dimensional Schr\"odinger operator with a strong magnetic field; here $h$ and $\mu$ are Plank and…
I consider magnetic Schr\"odinger operator in dimension $d=2$ assuming that coefficients are smooth and magnetic field is non-degenerating. Then I extend the remainder estimate $O(\mu^{-1}h^{-1}+1)$ derived in \cite{Ivr1} for the case when…
I consider the same operator as in part I assuming however that $\mu \ge Ch^{-1}$ and $V$ is replaced by $(2l+1)\mu h F+W$ with $l\in \bZ^+$. Under some non-degeneracy conditions I recover remainder estimates up to $O \bigl(\mu^{-{\frac 1…
Survey: In this paper I consider sharp spectral asymptotics for multidimensional magnetic Schr\"odinger operator with irregular coefficients with respect to two parameters -- semiclassical parameter $h$ and coupling parameter $\mu$. There…
We consider 2- and 3-dimensional Schr\"odinger or generalized Schr\"odinger-Pauli operators with the non-degenerating magnetic field in the open domain under certain non-degeneracy assumptions we derive pointwise spectral asymptotics. We…
We consider a magnetic Schr\"odinger operator $H^h$, depending on a semiclassical parameter $h>0$, on a compact Riemannian manifold. We assume that there is no electric field. We suppose that the minimal value $b_0$ of the intensity of the…
We revisit the problem of semiclassical spectral asymptotics for a pure magnetic Schr\"odinger operator on a two-dimensional Riemannian manifold. We suppose that the minimal value $b_0$ of the intensity of the magnetic field is strictly…
We consider a magnetic Schr\"odinger operator $H^h$, depending on the semiclassical parameter $h>0$, on a two-dimensional Riemannian manifold. We assume that there is no electric field. We suppose that the minimal value $b_0$ of the…
In this paper, we consider the 2D- Schr\"odinger operator with constant magnetic field $H(V)=(D_x-By)^2+D_y^2+V_h(x,y)$, where $V$ tends to zero at infinity and $h$ is a small positive parameter. We will be concerned with two cases: the…
We provide a leading order semiclassical asymptotics of the energy of bound states for magnetic Neumann Schr\"odinger operators in two dimensional (exterior) domains with smooth boundaries. The asymptotics is valid all the way up to the…
Sharp spectral asymptotics for multidimensional Schroedinger operators with the strong magnetic field are derived under rather weak smoothness conditions. I assume that magnetic intensity matrix has constant defect r>0 at each point. In…
We consider the spectral problem for the two-dimensional Schr\"odinger operator for a charged particle in strong uniform magnetic and periodic electric fields. The related classical problem is analyzed first by means of the…
We study the Schroedinger operator with a constant magnetic field in the exterior of a two-dimensional compact domain. Functions in the domain of the operator are subject to a boundary condition of the third type (Robin condition). In…
We continue our study of a magnetic Schr\"odinger operator on a two-dimensional compact Riemannian manifold in the case when the minimal value of the module of the magnetic field is strictly positive. We analyze the case when the magnetic…
We consider Schr\"odinger operators $H^h = (ih d+{\bf A})^* (ih d+{\bf A})$ with the periodic magnetic field ${\bf B}=d{\bf A}$ on covering spaces of compact manifolds. Under some assumptions on $\bf B$, we prove that there are arbitrarily…
Sharp spectral asymptotics for 2- and 3-dimensional Schroedinger operators with strong magnetic field are derived under rather weak smoothness conditions. In comparison with version 1 of 2005 new results are added and minor errors…