Analog of Levinson's formula for a Schrödinger operator with long-range potential
Trace formulas of order zero are obtained for a radial Schrödinger operator with long-range potential V(x) that decreases as \(x\to \infty\) as the power \(x^{-\alpha}\) with \(1\leq \alpha \leq 2\). These formulas relate the increment of the phase shift in the continuum to the characteristics of the discrete spectrum and generalize Levinson's theorem to the case of slowly decreasing potentials.
scientific article; zbMATH DE number 4015266