CHINESE JOURNAL OF PHYSICS VOL. 38, NO. 3-I JUNE 2000

Time Evolution of Free-Field Spatial Moments in Relativistic Quantum Mechanics: (II) Massive Case

Y. A. Kanev and K. R. Brownstein

Department of Physics and Astronomy,

University of Maine Orono, ME 04469-5709, U.S.A.
(Received November 9, 1999)

The explicit solution for the time evolution of the Nth rank spatial moment

$$\ds\int\tilde{\Psi}r^{j_1}r^{j_2}\cdots r^{j_N}d^3x$$

(r^j is the jth cartesian component of the position vector $\vec{r}$) of some field $\tilde{\Psi}(\vec{r},t)$ has been obtained. $\tilde{\Psi}$ can be any spatially bounded massive field satisfying a relativistic first order linear (``Dirac-like'') differential equation, such as the Dirac bi-spinor. The solution for the Nth moment is a ``polynomial'' in time of degree N, whose coefficients are oscillatory functions with only the frequency $\omega =mc^2/\hbar$ being present. The spin of the field $\tilde{\Psi}$ does not affect the form of the solution.

PACS. 03.65.Pm - Relativistic wave equations.
PACS. 03.50.-z $\;\,$- Classical field theory.
PACS. 03.65.-w $\,$- Quantum mechanics.

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