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Analytical approximation to the solution of the Dirac equation with the Eckart potential including the spin-orbit coupling term. (English) Zbl 1220.81101

Summary: By using the supersymmetric WKB approximation approach and the functional analysis method, we solve approximately the Dirac equation with the Eckart potential for the arbitrary spin-orbit quantum number \(\kappa \). The bound state energy eigenvalues and the associated two-component spinors of the Dirac particles are obtained approximately.

MSC:

81Q05 Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics
81Q60 Supersymmetry and quantum mechanics
81Q20 Semiclassical techniques, including WKB and Maslov methods applied to problems in quantum theory
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