Abstract:
Trace formulas of zeroth order 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 $1\leqslant\alpha\leqslant 2$. 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.
Fulltext:
PDF file (1022 kB)
