2013/02/05 by A. S. Larkin, V. S. Filinov
Physics and Astronomy · #quant-ph
paper · pdf · doi:10.1016/j.physleta.2013.03.019
10 pages, 26 figures. arXiv admin note: text overlap with arXiv:hep-th/0110114, arXiv:hep-ph/0501268, arXiv:math-ph/0702082 by other authors
arxiv created 2013/02/05 · arxiv updated 2015/06/12
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.