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It was long believed that there is a zero-point energy in the form ofh\omega/2 for massive particles, which is obtained from Schr\"odinger equationfor the harmonic oscillator model. In this paper, it is shown, by the Diracoscillator, that there is no such a zero-point energy. It is argued that when aparticle's wave function can spread in the whole space, it can be static. Thisdoes neither violate wave-particle duality nor uncertainty relationship. Diracequation correctly describes physical reality, while Schr\"odinger equationdoes not when it is not the nonrelativistic approximation of Dirac equationwith a certain model. The conclusion that there is no zero-point energy in theform of h\omega/2 is applied to solve the famous cosmological constant problemfor massive particles.

There is no vacuum zero-point energy in our universe for massive particles within the scope of relativistic quantum mechanics