Abstract: The principle of phase invariance （also called ＂phase harmonic law＂） in classical wave dynamics as a basic physical principle is discussed and an underlying intuitive reason which lies behind it the order invariance of physical quantities is proposed. Such invariance reflects the principle of relativity. From ＂phase harmonic law＂ we deduced the transformation laws for wave vector, frequency, and group velocity of wave packets while space- time coordinates satisfying Galileo and Lorentz transformation, respectively. Furthermore we discussed the problem of phase transformation for Schroedinger equation and Klein Gordon equation. For Schroedinger equation, we believe that the complex nature of wave function releases the wave function from phase invariance which is inevitable for classical waves （where only the real part of wave function have physical meaning）, thus expanded the physical region. It becomes the basic quantum equation of nonrelativistic particles. Klein - Gordon equation, however, satisfies ＂phase harmonic law＂, we believe that there should be some kind of order invariance for physical quantities behind it. We discussed one possibility from professor Guangjiong Ni＇s two-component （particle and antiparticle） notion to identify such an order.

Key words: phase harmonic law, classical wave, quantum wave, order invariance, Schroedinger equation, Klein- Gordon equation