A note on the Schrödinger operator with a long-range potential

2018/10/07 by Yafaev, D. R.
#34E20 #34L10 #34L15 #47A40 #81U05 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #FOS: Physical sciences #Functional Analysis (math.FA) #Mathematical Physics (math-ph) #Spectral Theory (math.SP)

paper · doi:10.48550/arxiv.1810.03112

Abstract

Our goal is to develop spectral and scattering theories for the one-dimensional Schrödinger operator with a long-range potential q(x), x≥ 0. Traditionally, this problem is studied with a help of the Green-Liouville approximation. This requires conditions on the first two derivatives q' (x) and q'' (x). We suggest a new Ansatz that allows us to develop a consistent theory under the only assumption q' ∈ L¹.

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