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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References
Aron J C 1979Found. Phys. USA9 163
Birula I B 1971aPhys. Rev. D3 2410
Birula I B 1971bPhys. Rev. 2413
Bohm D 1952Phys. Rev. 85 166
Depaquit S, Guret P H and Vigier J P 1972Int. J. Theor. Phys. 4 19
Féynman R P 1961 InQuantum Electrodynamics W A Benjamin Inc. Reading Mass.
Gutler R and Hestenes D 1975J. Maths. Phys. 16 573
Hestenes D 1973J. Math. Phys. 14 893
Hestenes D 1975J. Math. Phys. 16 556
Hestenes D 1979Am. J. Phys. 47 399
Hirschfelder J O, Christoph A C and Palke W E 1974J. Chem 61 5433
Ichiyanagi M 1979J. Phys. Soc. Jpn. 47 755
Jehle H 1968Int. J. Quantum Chem. IIS 373
Jehe H 1969Int. J. Quantum Chem. III 269
Landau L 1945J. Phys. 17 310
Lehr W J and Park J L 1977J. Math. Phys. 18 1235
Madelung E 1926Z. Phys. 40 322
McDonald A H 1979J Phys. C12 2977 and references therein
Messiah A 1962 InQuantum Mechanics (Amsterdam: North Holland) Vol II pp. 950
Nelson E 1966Phys. Rev. 150 1079
Pavlik P I and Blinder S M 1967J. Chem. Phys. 46 2749
Petroni C N and Vigier J P 1981Phys. Lett. A81 12
Pitzer K S 1979Acc. Chem. Res. 12 271
Pyykkö P and Desclaux J P 1979Acc. Chem. Res. 12 276
Rajagopal A K 1980Adv. Chem. Phys. XLI 59
Riess J 1970Phys. Rev. D2 647
Riess J and Primas H 1968Chem. Phys. Lett. 1 545
Rose M E 1957 InElementary Theory of Angular Momentum (New York: John Wiley)
Schiff L I 1968 InQuantum Mechanics (New York: McGraw Hill) pp. 180
Sucher J 1980Phys. Revs. A22 348 and references therein
Wong C Y 1976J. Math. Phys. 17 1008
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Datta, S.N. Fluid-dynamical representations of the Dirac equation. Pramana - J Phys 20, 251–265 (1983). https://doi.org/10.1007/BF02846218
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DOI: https://doi.org/10.1007/BF02846218