A bound state of the Schrodinger system is disturbed by an additional
potential. It is shown that the system is still in a bound state if an
d only if its energy correction is restricted to the corresponding val
ue. This infers some previous series solutions in quantum mechanics to
be unbound states for the order i > 1 of perturbation. The corrected
bound states of the system are given and their physical meaning is dis
cussed simply. Application of the method to Stark effect reveals its a
dvantage for researches of quantum chaos.