On the conventional and modified WKB approximation with a singular potential

Abstract

In the first part of this paper an analytical expression in term of the quantum numberl of the conventional WKB phase shift for singular potentials (i.e. V(r)=Anr−n,n≥3) is derived. It is shown that the asymptotic form of this expression for high values ofl as well as for low energies agrees with well-known results. In the second part the modified WKB approach is discussed to the «zero» and «first» order approximation where the connection between the conventional and the modified approaches is underlined. A general expression of the modified phase shift is obtained. It is also shown that, in the case of low energies, its asymptotic form agrees well with results obtained by other authors.