The Dirac Equation Without Spin-Orbit Coupling

1 The Dirac Equation Without Spin-Orbit Coupling 

For atoms with high atomic numbers it is important that relativistic effects are included in the band-structure calculations. In SCFC we therefore solve the Dirac rather than the Schrodinger equation, but leave out the spin-orbit interaction. In doing so we obtain an effective one-electron equation which is essentially the Schrodinger equation with the important mass-velocity and Darwin corrections included. The present technique is based on unpublished work by O.K. Andersen and U.K. Poulsen. KoelUng and Harmon [9.8] have taken a related approach. 

The equations for the two radial wave functions g and f in the Dirac central field problem are [9.9,10] 

We note that the usual Pauli equation is obtained from (9.31) in the ap- 2 

We now wish to have once more two coupled first-order differential equations similar to (9.30). To this end we define the functions 

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C SOLVES THE DIRAC EQUATIONS WITHOUT SPIN-ORBIT COUPLING AND ... 

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