  The integral Wigner - Liouwille equation describing time evolution of the
semi-relativistic quantum 1D harmonic oscillator have been exactly solved by
combination of the Monte-Carlo procedure and molecular dynamics methods. The
strong influence of the relativistic effects on the time evolution of the
momentum, velocity and coordinate Wigner distribution functions and the average
values of quantum operators have been studied. Unexpected 'protuberances' in
time evolution of the distribution functions were observed. Relativistic proper
time dilation for oscillator have been calculated.
