Abstract: With the help of principle of superposition in quantum mechanics and the operator splitting method, we study the movement of the center position of the initial Gaussian wave packet in one-dimensional harmonic oscillator potential. The results show that its quantum evolution performs characteristics of a classical harmonic oscillator; the initial location and the initial momentum of the wave packet play a similar role as the classical oscillator. Our results should be helpful to understand the Gaussian wave packet method, which is commonly applied in the research on complex quantum system.

Key words: one-dimensional harmonic oscillator, principle of superposition, operator splitting method, FFT