Simplified solution of the Dirac equation with a Coulomb potential

Abstract
It is shown that the Dirac equation with a Coulomb potential has a simplified solution where each component contains one term of a confluent hypergeometric function only instead of two terms. This solution reduces to the usual free-field solution when the Coulomb potential is turned off. Thus the Dirac Coulomb equation has a solution which is not very different from the corresponding Schrödinger or Klein-Gordon equations.

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