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We generalized the squeeze and displacement operators of the one-dimensionalharmonic oscillator to the three-dimensional case and based on these operatorswe construct the corresponding coherent and squeezed states. We have alsocalculated the Wigner function for the three-dimensional harmonic oscillatorand from the analysis of time evolution of this function, the quantum Liouvilleequation is also presented. Further properties of the quantum states includingMandel's Q and quadrature squeezing parameters are discussed as well.

Displacement and Squeeze Operators of a Three-Dimensional Harmonic Oscillator and Their Associated Quantum States