Fluid-dynamical representations of the Dirac equation |
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Authors: | Sambhu N Datta |
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Institution: | (1) Department of Chemistry, Indian Institute of Technology, Powai, 400 076 Bombay, India |
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Abstract: | A relative kinetic mass operator is defined bym =c
−2·(E −eΦ), and it is shown that bt using it in a symmetric form one can correlate the (charge) velocity operatorα in the Dirac theory exactly with the general quantum mechanical momentum —ih∇. Then the net force, defined as the rate of change of the relative momentum with time, is exactly equal to the Lorentz force.
The contribution due to the time variation of mass equals the negative of space variation of the scalar potential, the Newtonian
force, whereas the time variation of the charge current absorbs the entire vector potential dependence. The analogous Euler
equations can be written either in terms of the charge current or in terms of the mass current. For a many particle system
one needs the usual net single particle parameters and the consideration of both the direct and exchange contributions of
the two particle interaction. These Euler equations yield two different conditions of the stationary state. It is shown that
the charge-current condition is necessary but not sufficient, whereas the mass-current condition retains the appropriate scalar
potential dependence. These two conditions are compared for the spherically symmetric case. The charge density, charge current
and relative mass current are tabulated for atomic spinors. Differences between the quantum and classical forces for the H
2
+
molecular ion exhibit the inadequacy of ordinary atomic spinor basis in forming molecular spinors. |
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Keywords: | Relativistic fluid dynamics kinetic mass force Euler equation |
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