Abstract: The Lie symmetries and conserved quantities of the three-dimensional anisotropic harmonic oscillator are studied. When ω1/ω2/ω3 is equal to 3/2/1 and 4/3/1 , respectively, the Lie symmetries and conserved quantities of two typical three-dimensional anisotropic harmonic oscillators are also studied, and seven conserved quantites are obtained. By discussing the independence of the conserved quantities, we find that only five of them are independent.

Key words: three-dimensional anisotropic harmonic oscillator, Lie symmetries, independent conserved quanlities