Extrapolation technique from mixed and variational estimators
The one body density matrix (3.84) corresponds to a
mixed estimator, when the averaging of the variable is
done in an asymmetric way
.
If the trial wavefunction is close to the true ground-state
wavefunction one can estimate the ground-state average
by using the following
technique.
Let us denote the difference between the trial wave function and
ground-state wave function as
(3.89)
Then the ground-state average can be written as
(3.90)
If is small the second order term
can be neglected.
After substitution
the extrapolation formula becomes