Abstract: A qubit is formed by overlapping the ground state and the second excited state of single electron in one-dimensional parabolic potential and the property of qubit is studied. The numerical calculations show that the probability density distribution of electron in qubit varies with varying space coordinate, its amplitude is maximal in the equilibrium and smaller in other positions. It is also shown that the probability density of electron in all space point oscillate periodically with time and the oscillating period is determined by the character of parabolic potential.

Key words: parabolic potential, energy eigenequation, wave function, qubit