DOI: https://doi.org/10.30970/jps.09.1
WKB METHOD FOR THE DIRAC EQUATION WITH VECTOR AND SCALAR POTENTIALS
V. Yu. Lazur, V. V. Rubish, O. K. Reity
Uzhgorod National University, 32 Voloshyna St.,
Uzhgorod,
UA-88000, Ukraine
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Journal of Physical Studies 9(1), 1–18 (2005)
DOI: https://doi.org/10.30970/jps.09.1 WKB METHOD FOR THE DIRAC EQUATION WITH VECTOR AND SCALAR POTENTIALSV. Yu. Lazur, V. V. Rubish, O. K. Reity
Uzhgorod National University, 32 Voloshyna St., |
|
A sequential scheme of the WKB method is developed for the Dirac equation in a central symmetrical field with scalar and vector variants of interaction. The view of relativistic wave functions in the classical allowed and forbidden regions, and the conditions of their matching at transition through the turning points are found. As applications of the developed method the relativistic analogu of Bohr-Sommerfeld quantization condition which contains a spin-orbital interaction in a mixture of scalar $S(r)$ and vector $V(r)$ potentials, and relativistic generalization of the Gamov formula for quasistationary level width of the spin 1/2 particle interacting with scalar and vector fields simultaneously are obtained. It is shown that for Coulomb and oscillator potentials with the mixed Lorentz structure the obtained rule of quantization exactly reproduces the energy spectrum.
PACS number(s): 03.65.Ge, 03.65.Pm, 03.65.Sq