Abstract: B-spline function is used to solve numerically the energy eigenvalue of electrons in hydrogen atom under the interference of random potential field. The eigen energy and eigen wave function of electrons in hydrogen atom in the case of random potential with different amplitude range are calculated. The results show that the probability of electron distribution changes more frequently when the range of stochastic potential is larger. And the more quantum numbers there are, the more unstable the system becomes, and the more easily the central force field is destroyed by the applied stochastic potential field.

Key words: quantum physics, hydrogen atom, B-spline, random potential field, eigen energy, eigen wave function