Título del libro: Chemical Physics Research Developments
Título del capítulo: On sum rulesand recurrence relations for matrix elementsin relativistic quantum mechanics
ALVARO LORENZO SALAS BRITO; RODOLFO PATRICIO MARTINEZ Y ROMERO;
Autores externos:
Idioma:
Inglés
Año de publicación:
2011
Resumen:
We review recent attempts aimed at the recursive calculations of radial matrix elements in relativistic quantum mechanics. We first discuss how to obtain sum rules relating matrix elements of f and of ?f with matrix elements of their first and second derivatives -f is an arbitrary radial function and ? is the stand ard Dirac matrix. Such elements are assumed to be taken between radial energy eigenfunctions corresponding to two different radial potentials V1(r) and V2(r) in the unshifted case. That is, the validity of our obtained relations requires that both potentials attain a minimum at the same radial position. To obtain directly usable results we then insert in our general formulas specific expressions for the two radial potentials and a definite form of the radial function to obtain recurrence relations between the relativistic matrix elements of the mentioned function. We give specific examples of such procedure obtaining both new and previously reported recurrence relations between matrix elements of powers of the radial coordinate, r? and ?r?, where ? can in general be a complex number, between radial hydrogenic states. We also obtain recurrence relations for two center matrix elements of r? in potential energy functions of the form Vi(r) = air?i, i = 1,2, where ai and ?i are constants. © 2011 by Nova Science Publishers, Inc. All rights reserved.
Entidades citadas de la UNAM:
ISBN:
9781611220681
Editorial:
Nova Science Publishers, Inc. Nombre de la publicación:
On sum rulesand recurrence relations for matrix elementsin relativistic quantum mechanics
Página inicial:
257
Página final:
276
Tipo de producto:
Capítulo de un Libro
