Saddle-point technique for inner-shell-vacancy problems in quantum mechanics

In this paper a theorem is proved which shows that a physical system with an inner-shell vacancy corresponds to the saddle-point energy solution in the Rayleigh-Ritz variation method if the vacancy is built explicitly into the wave function. This enables us to calculate the inner-shell-vacancy states of a many-body system from first principles. This method is very easy to use and should be applicable to many areas of physics.