Application of Hypervirial Theorem As Criteria For Accuracy of Variational Trial Wave Function

It would be interesting to investigate the accuracy of the results obtained in the variational method, because it is important for studying hadron spectra. One can define some criteria to judge the accuracy, or the quality of the trial function. We employ a simple potential form to check how accurate the variational results obtained by a single-parameter trial function can be. All the concerned problems, in particular, the relevant aspects on the application of hypervirial theorem in variational method for various potential forms, are discussed in every detail. The qualitative conclusion of the work can be generalized to much more complicated cases. Our study suggests that the hypervirial relations can serve as a good and practical criterion for judging the accuracy of any trial functions.