Abstract
The Dirac equation with a scalar linear potential is solved analytically. Analytical solutions are shown to exist when there are some quantitative relations between the strength constant of the linear potential and the mass of the particle. The analytical solutions are assumed to be of asymptotic form times a polynomial expression for the radial coordinate r. Actual solutions are found up to the order of r5.
Highlights
Analytical solutions are shown to exist when there are some quantitative relations between the strength constant of the linear potential and the mass of the particle
We look for analytical solutions of the Dirac equation with a scalar linear potential
We investigate the Dirac equation of a particle with mass moving in a central scalar linear potential
Summary
Hirokazu Tezukaa Natural Science Laboratory, Toyo University, Tokyo 112-8606, Japan (Received 20 June 2013; accepted 19 August 2013; published online 29 August 2013). The Dirac equation with a scalar linear potential is solved analytically. Analytical solutions are shown to exist when there are some quantitative relations between the strength constant of the linear potential and the mass of the particle.
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