The Dirac equation in the algebraic approximation. IV. Application of the partitioning technique

It is shown that the application of the partitioning technique to the Dirac equation in the algebraic approximation has a number of advantages: (i) a correct matrix representation of the Schrodinger equation is obtained in the limit c to infinity ; (ii) the positive and negative energy solutions are separated; (iii) it has variational properties which are independent of the choice of basis sets for parametrisation of the large and small components of the relativistic wavefunction; (iv) a relativistic generalisation of the bracketing function can be obtained, (v) it leads to improved numerical accuracy. These advantages of the partitioned Dirac equation are illustrated by means of prototype calculations.