Solutions, Spectrum, and Dynamica for Schrödinger Operators on Infinite Domains
| dc.creator | Kiselev, Alexander | |
| dc.creator | Last, Yoram | |
| dc.date | 1999-06-02 | |
| dc.date.accessioned | 2026-07-07T05:29:21Z | |
| dc.date.available | 2026-07-07T05:29:21Z | |
| dc.description | Let H be a Schrödinger operator defined on an unbounded domain D in R^d with Dirichlet boundary conditions (D may equal R^d in particular). Let u(x,E) be a solution of the Schrödinger equation (H-E)u(x,E)=0, and let B_R denote a ball of radius R centered at zero. We show relations between the rate of growth of the L^2 norm \|u(x,E)\|_{L^2(B_R \cap D)} of such solutions as R goes to infinity, and continuity properties of spectral measures of the operator H. These results naturally lead to new criteria for identification of various spectral properties. We also prove new fundamental relations berween the rate of growth of L^2 norms of generalized eigenfunctions, dimensional properties of the spectral measures, and dynamical properties of the corresponding quantum systems. We apply these results to study transport properties of some particular Schrödinger operators. | |
| dc.description | 28 pages, 1 figure | |
| dc.identifier | https://arxiv.org/abs/math/9906021 | |
| dc.identifier | http://arxiv.org/abs/math/9906021 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/78607 | |
| dc.subject | Spectral Theory | |
| dc.subject | Mathematical Physics | |
| dc.subject | Analysis of PDEs | |
| dc.subject | 35J10, 81Q10; 35P05 | |
| dc.title | Solutions, Spectrum, and Dynamica for Schrödinger Operators on Infinite Domains | |
| dc.type | text |