Eigenvalue Asymptotics for a Schrödinger Operator with Non-Constant Magnetic Field Along One Direction

Nonclassical Eigenvalue Asymptotics for Operators of Schrödinger

which depends on the volume u)n of the unit sphere in R n and the beta function. Assuming /3 < 2 we see that integral (2) becomes divergent if V (x) vanishes to a sufficiently high order. The simplest such potential is V(x,y) = \x\\y\P o n R n + R m . The Weyl (volume counting) principle, when applied to the corresponding Schrödinger operator — A-hV(x), fails to predict discrete spectrum below ...

On Non - Linear Schrödinger Equation with Magnetic Field

We study the non-linear Schödinger equation with time depending magnetic field without smallness assumption at infinity. We obtain some results on the Cauchy problem, WKB asymptotics and instability.

Steady Mixed Convection Flow of Water at 4◦C Along A Non-Isothermal Vertical Moving Plate with Transverse Magnetic Field

Eigenvalue asymptotics for the Schrödinger operator with a δ-interaction on a punctured surface

Given n ≥ 2, we put r = min{ i ∈ N; i > n/2 }. Let Σ be a compact, Cr-smooth surface in Rn which contains the origin. Let further {Sǫ}0≤ǫ<η be a family of measurable subsets of Σ such that supx∈Sǫ |x| = O(ǫ) as ǫ → 0. We derive an asymptotic expansion for the discrete spectrum of the Schrödinger operator −∆−βδ(·−Σ\Sǫ) in L2(Rn), where β is a positive constant, as ǫ → 0. An analogous result is g...

The Spectral Asymptotics of the Two-dimensional Schrödinger Operator with a Strong Magnetic Field

We consider the spectral problem for the two-dimensional Schrödinger operator for a charged particle in strong uniform magnetic and periodic electric fields. The related classical problem is analyzed first by means of the Krylov-Bogoljubov-Alfven and Neishtadt averaging methods. It allows us to show “almost integrability” of the the original two-dimensional classical Hamilton system, and to red...