Zero-range interaction in arbitrary dimensions and in the presence of external forces

Abstract

We analyze zero-range interactions in arbitrary dimensions and in the presence of external forces in terms of non-local separable potentials. We show that in one-, two- and three-dimensional cases this approach is equivalent to the standard method with a renormalization operator. Our analysis indicates that the method of a projection operator is also useful for studying processes occurring under the influence of additional forces. As an example we present exact solutions for a particle interacting with a static electric field.