Separation of Dirac equation

Solutions to the Dirac equation in a spherically symmetric potential U r) for a state with energy e and angular momentum quantum numbers (k to) take the form 

We find, with the help of the identities (13,15), that the radial functions PK r) and QK(r) satisfy the coupled first-order differential equations  

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P.-O. Lowdin. Studies in Perturbation Theory Part VIII. Separation of Dirac equation + Study of Spin-Orbit Coupling + Fermi Contact Terms. J. Mol. Spectrosc., 14(2) (1964) 131-144. 

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