Variational estimation of the wave function at the origin for heavy quarkonium

Abstract

In the framework of the nonrelativistic potential model, the variational method, especially the selection of the trial wave function (TWF) is studied via the calculations of energy eigenvalues and wave functions at the origin (WFO) in heavy quarkonium systems. As a result, a more efficient way to construct the TWF is found. With this TWF, the accuracy of the squared WFO can be of the same order as that of the corresponding energy eigenvalue. The relation between the WFO and the reduced mass is also investigated. The resultant formulas agree with those deduced from the general arguments for the power-law potentials. [S0556-2821(99)02213-4].