Eur. Phys. J. D 53, 41-50 (2009)
https://doi.org/10.1140/epjd/e2009-00074-0

Exact solutions of the Schrödinger equation for zero energy

Universität Oldenburg, Institut für Physik, 26111 Oldenburg, Germany

Corresponding author: ^a jochen.pade@uni-oldenburg.de

Received: 10 July 2008
Revised: 19 December 2008
Published online: 6 March 2009

Abstract

Some new exact solutions of the Schrödinger equation for zero energy are presented for certain nontrivial model potentials. Exact expressions for the different scattering lengths are derived and their differences and similarities are worked out. In particular, the respective distributions of the zeros and poles of the scattering lengths are characterized in detail.