  We regard the Wheeler-De Witt equation as a Sturm-Liouville problem with the
cosmological constant considered as the associated eigenvalue. The used method
to study such a problem is a variational approach with Gaussian trial wave
functionals. We approximate the equation to one loop in a Schwarzschild
background. A zeta function regularization is involved to handle with
divergences. The regularization is closely related to the subtraction procedure
appearing in the computation of Casimir energy in a curved background. A
renormalization procedure is introduced to remove the infinities together with
a renormalization group equation.
