An asymptotic expansion for the quarkonium reduced wavefunction at the origin

Abstract

Equating two different representations, in the form of a Born series and the spectral one, of the euclidean time-dependent Green's function for the Schrödinger equation with a general power-law confining potential we obtain an asymptotic expansion for the quarkonium reduced (i.e. divided by r l ) radial wavefunction at the origin in inverse powers of the binding energy. The leading term of this expansion coincides with analogous results obtained by other authors within the framework of the WKB approximation.