The Dirac equation in the algebraic approximation. IV. Application of the partitioning technique
John H. Wood, Ian Philip Grant, Stephen S. Wilson · Journal of Physics B Atomic and Molecular Physics · 1985
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.