Scattering by singular logarithmic potential

Abstract

Potential of the form (gr-4 ln2 r - g1/2r -3)θ(r - r0) is considered in connection with the applicability of peratization technique. The advantage of this potential is the fact that while it is dominated by a logarithmic part near the origin, the exact solution of the zero-energy and s-wave Schrödinger equation is obtained in a closed form. We show that the peratization technique gives the correct answers.