The Schrödinger equation on spheres
نویسندگان
چکیده
منابع مشابه
On Bound States Concentrating on Spheres for the Maxwell-Schrödinger Equation
We study the semiclassical limit for the following system of Maxwell-Schrr odinger equations: waves for the nonlinear Schrr odinger equation interacting with the electrostatic eld: the unknowns v and represent the wave function associated to the particle and the electric potential respectively. By using localized energy method, we construct a family of positive radially symmetric bound states (...
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is a distribution on R×Sd with fairly nasty behavior; its singular support is all of R×Sd. However, J. Rauch pointed out to me that when d = 1 and t is a rational multiple of π (we say t ∈ πQ), then e−it∆δ(x) ∈ D′(S1) is a finite sum of delta functions on S1. Hence for such t ∈ πQ, e−it∆ is bounded on Lp(S1) for each p ∈ [1,∞]. Here we work out an equally precise description of e−it∆ on D′(Sd),...
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ژورنال
عنوان ژورنال: Pacific Journal of Mathematics
سال: 2003
ISSN: 0030-8730
DOI: 10.2140/pjm.2003.209.145