Ja. Reyes et al., Impurity at the boundary of two quantum wires: 1D Schrodinger equations with an asymmetric Coulumb potential., HELV PHYS A, 72(5-6), 1999, pp. 295-300
In the momentum space we find the bound eigenenergies and eigenfunctions of
the ID Schrodinger equation for an asymmetric Coulomb potential. We find t
hat eigenfunctions in the configuration space are expressed in terms of fra
ctional derivatives. Our approach could provide qualitative features of the
electronic states of an impurity located between two different quantum wir
es.