Calculation of matrix elements in relativistic quantum mechanics

Abstract

Employing a relativistic version of a hypervirial result, recurrence relations for arbitrary nondiagonal radial hydrogenic matrix elements have recently been obtained in Dirac relativistic quantum mechanics. In this contribution honoring Professor Lowdin, we report on a new relation we have recently discovered between the matrix elements <2\r(lambda)\1> and <2\betar(lambda)\>-where beta is a Dirac matrix and the numbers distiguish between different radial eigenstates-that allow for a simplification and hence for a more convenient way of expressing the recurrence relations. We additionally derive another relation that can be employed for simplifying two-center matrix element calculations in relativistic atomic or molecular calculations. (C) 2002 Wiley Periodicals, Inc. Int.