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