  We study the extraction of the ground-state parameters from vacuum-to-vacuum
correlators. We work in quantum-mechanical potential model which provides the
only possibility to probe the reliability and the actual accuracy of this
method: one obtains the bound-state parameters from the correlators by the
standard procedures adopted in the method of sum rules and compares these
results with the exact values calculated from the Schroedinger equation. We
focus on the crucial ingredient of the method of sum rules - the effective
continuum threshold - and propose a new algorithm to fix this quantity. In a
quantum-mechanical model, our procedure leads to a remarkable improvement of
the accuracy of the extracted ground-state parameters compared to the standard
procedures adopted in the method and used in all previous applications of
dispersive sum rules in QCD. The application of the proposed procedure in QCD
promises a considerable increase of the accuracy of the extracted hadron
parameters.
