2022/11/18 by Ascione, Giacomo, Lőrinczi, József
#35R11 #47A75 #Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Primary 47D08 #Secondary 47G20 #Spectral Theory (math.SP)
paper · doi:10.48550/arxiv.2211.10093
In a first part of this paper we investigate the continuity (stability) of the spectrum of a class of non-local Schrödinger operators on varying the potentials. By imposing conditions of different strength on the convergence of the sequence of potentials, we give either direct proofs to show the strong or norm resolvent convergence of the so-obtained sequence of non-local Schrödinger operators, or via Γ-convergence of the related positive forms for more rough potentials. In a second part we use these results to show via a sequence of suitably constructed approximants that the ground states of massive or massless relativistic Schrödinger operators with spherical potential wells are radially decreasing functions.