Bound States of the Perturbed Schrödinger Systems

A bound state of the Schrödinger system is disturbed by an additional potential. It is shown that the system is still in a bound state if and only if its energy correction is restricted to the corresponding value. 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 discussed simply. Application of the method to Stark effect reveals its advantage for researches of quantum chaos.