Asymptotics and estimates of the discrete spectrum of the Schrodinger operator on a discrete periodic graph

2019/03/28 by Korotyaev, Evgeny, Sloushch, Vladimir · 1 citation
#FOS: Mathematics #Spectral Theory (math.SP)

paper · doi:10.48550/arxiv.1903.11810

Abstract

The periodic Schrodinger operator H on a discrete periodic graph is considered. We estimate the discrete spectrum of the perturbed operator H _ - (t) = H-tV , t> 0 , where the potential V ge 0 is decreasing and t>0 is the coupling constant. If the potential has a power asymptotics at infinity, then we obtain asymptotics of the discrete spectrum of operator H_ - (t) with a large coupling constant.

Cited by

• Scattering for time periodic Hamiltonians on graphs

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