ترغب بنشر مسار تعليمي؟ اضغط هنا

Dispersion Estimates for Spherical Schrodinger Equations: The Effect of Boundary Conditions

78   0   0.0 ( 0 )
 نشر من قبل Gerald Teschl
 تاريخ النشر 2016
  مجال البحث فيزياء
والبحث باللغة English




اسأل ChatGPT حول البحث

We investigate the dependence of the $L^1to L^infty$ dispersive estimates for one-dimensional radial Schro-din-ger operators on boundary conditions at $0$. In contrast to the case of additive perturbations, we show that the change of a boundary condition at zero results in the change of the dispersive decay estimates if the angular momentum is positive, $lin (0,1/2)$. However, for nonpositive angular momenta, $lin (-1/2,0]$, the standard $O(|t|^{-1/2})$ decay remains true for all self-adjoint realizations.



قيم البحث

اقرأ أيضاً

We derive a dispersion estimate for one-dimensional perturbed radial Schrodinger operators where the angular momentum takes the critical value $l=-frac{1}{2}$. We also derive several new estimates for solutions of the underlying differential equation and investigate the behavior of the Jost function near the edge of the continuous spectrum.
We study Schroedinger operators with Robin boundary conditions on exterior domains in $R^d$. We prove sharp point-wise estimates for the associated semi-groups which show, in particular, how the boundary conditions affect the time decay of the heat k ernel in dimensions one and two. Applications to spectral estimates are discussed as well.
We derive dispersion estimates for solutions of the one-dimensional discrete perturbed Dirac equation. To this end we develop basic scattering theory and establish a limiting absorption principle for discrete perturbed Dirac operators.
We show that for a one-dimensional Schrodinger operator with a potential whose (j+1)th moment is integrable the jth derivative of the scattering matrix is in the Wiener algebra of functions with integrable Fourier transforms. We use this result to im prove the known dispersive estimates with integrable time decay for the one-dimensional Schrodinger equation in the resonant case.
88 - Markus Holzmann 2020
In this note the three dimensional Dirac operator $A_m$ with boundary conditions, which are the analogue of the two dimensional zigzag boundary conditions, is investigated. It is shown that $A_m$ is self-adjoint in $L^2(Omega;mathbb{C}^4)$ for any op en set $Omega subset mathbb{R}^3$ and its spectrum is described explicitly in terms of the spectrum of the Dirichlet Laplacian in $Omega$. In particular, whenever the spectrum of the Dirichlet Laplacian is purely discrete, then also the spectrum of $A_m$ consists of discrete eigenvalues that accumulate at $pm infty$ and one additional eigenvalue of infinite multiplicity.
التعليقات
جاري جلب التعليقات جاري جلب التعليقات
mircosoft-partner

هل ترغب بارسال اشعارات عن اخر التحديثات في شمرا-اكاديميا