  We study the uncertainties of the determination of the ground-state
parameters from Shifman-Vainshtein-Zakharov (SVZ) sum rules, making use of the
harmonic-oscillator potential model as an example. In this case, one knows the
exact solution for the polarization operator $\Pi(\mu)$, which allows one to
obtain both the OPE to any order and the spectrum of states. We start with the
OPE for $\Pi(\mu)$ and analyze the extraction of the square of the ground-state
wave function, $R\propto|\Psi_0(\vec r=0)|^2$, from an SVZ sum rule, setting
the mass of the ground state $E_0$ equal to its known value and treating the
effective continuum threshold as a fit parameter. We show that in a limited
``fiducial'' range of the Borel parameter there exists a solution for the
effective threshold which precisely reproduces the exact $\Pi(\mu)$ for any
value of $R$ within the range $0.7 \le R/R_0 \le 1.15$ ($R_0$ is the known
exact value). Thus, the value of $R$ extracted from the sum rule is determined
to a great extent by the contribution of the hadron continuum. Our main finding
is that in the cases where the hadron continuum is not known and is modeled by
an effective continuum threshold, the systematic uncertainties of the sum-rule
procedure cannot be controlled.
