Vacuum Energy Estimates in Quantum Gravity and the Wheeler-DeWitt Equation

In the Wheeler-DeWitt framework, by a gauge fixing procedure, we set up a scheme to recover a Schr"odinger type equation, living in the orbits space with the {\it lapse} function as evolution parameter. By means of the associated stationary equation, we have the possibility of calculating quantum corrections to classical quantities. The Schwarzschild wormhole case is discussed as an example of application.