Abstract: Based on the wave functions of three-dimensional quantum linear harmonic oscillator in the Descartes and spherical coordinates, we make the sampling by Monte Carlo method through the spatial probability density function. The spatial probability cloud of the particle is visualized by Mathematica software in different coordinate systems. Further comparison and analyzation of the visualization pictures of the system from different decompositions of the quantum numbers in two coordinate systems are carried out. And the physical meaning is illustrated from the theoretical point of view of quantum mechanics.

Key words: quantum mechanics, quantum harmonic oscillator, Monte-Carlo method, visualization