A useful form of the recurrence relation between relativistic atomic matrix elements of radial powers

Recently obtained recurrence formulae for relativistic hydrogenic radial matrix elements are cast in a simpler and perhaps more useful form. This is achieved with the help of a new relation between the $r^a$ and the $\beta r^b$ terms ($\beta$ is a $4\times 4$ Dirac matrix and $a, b$ are constants) in the atomic matrix elements.Comment: 7 pages, no figure

Recurrence relation for relativistic atomic matrix elements

Recurrence formulae for arbitrary hydrogenic radial matrix elements are obtained in the Dirac form of relativistic quantum mechanics. Our approach is inspired on the relativistic extension of the second hypervirial method that has been succesfully employed to deduce an analogous relationship in non relativistic quantum mechanics. We obtain first the relativistic extension of the second hypervirial and then the relativistic recurrence relation. Furthermore, we use such relation to deduce relativistic versions of the Pasternack-Sternheimer rule and of the virial theorem.Comment: 10 pages, no figure

Arriba during the Spanish Transition : the abandonment of its propaganda function with respect to the Government

Durante la transición española, se produjeron cambios políticos, sociales, ideológicos y periodísticos en el país que contribuyeron a que el diario Arriba, fundado por Falange Española y asimilado como órgano de propaganda por el régimen franquista durante la dictadura, evolucionara considerablemente. Pasó, así, gracias a la presencia de diferentes ideologías en su redacción, del apoyo al Gobierno, aún muy presente tras la muerte de Franco (noviembre de 1975), a la crítica hacia el mismo al fin de este período, el referéndum de la Constitución (diciembre de 1978).During the Spanish transition, there were political, social and ideological, but also journalistic updates in the country, which caused the newspaper Arriba, founded by ‘Falange Española’ and assimilated as a propaganda organ by Franco’s regime during the dictatorship, evolved during the Spanish transition. Due to the incoming ideologies in its newsroom, the newspaper went from supporting the government after Caudillo’s death (November, 1975), to criticize it at the end of the period, during the referendum of the Constitution (December, 1978)

Arriba durante la Transición española: el abandono de su función propagandística con respecto al Gobierno

During the Spanish transition, there were political, social and ideological, but also journalistic updates in the country, which caused the newspaper Arriba, founded by ‘Falange Española’ and assimilated as a propaganda organ by Franco’s regime during the dictatorship, evolved during the Spanish transition. Due to the incoming ideologies in its newsroom, the newspaper went from supporting the government after Caudillo’s death (November, 1975), to criticize it at the end of the period, during the referendum of the Constitution (December, 1978).Durante la transición española, se produjeron cambios políticos, sociales, ideológicos y periodísticos en el país que contribuyeron a que el diario Arriba, fundado por Falange Española y asimilado como órgano de propaganda por el régimen franquista durante la dictadura, evolucionara considerablemente. Pasó, así, gracias a la presencia de diferentes ideologías en su redacción, del apoyo al Gobierno, aún muy presente tras la muerte de Franco (noviembre de 1975), a la crítica hacia el mismo al fin de este período, el referéndum de la Constitución (diciembre de 1978)

New non-unitary representations in a Dirac hydrogen atom

New non-unitary representations of the SU(2) algebra are introduced for the case of the Dirac equation with a Coulomb potential; an extra phase, needed to close the algebra, is also introduced. The new representations does not require integer or half integer labels. The set of operators defined are used to span the complete space of bound state eigenstates of the problem thus solving it in an essentially algebraic way

From circular paths to elliptic orbits: A geometric approach to Kepler's motion

The hodograph, i.e. the path traced by a body in velocity space, was introduced by Hamilton in 1846 as an alternative for studying certain dynamical problems. The hodograph of the Kepler problem was then investigated and shown to be a circle, it was next used to investigate some other properties of the motion. We here propose a new method for tracing the hodograph and the corresponding configuration space orbit in Kepler's problem starting from the initial conditions given and trying to use no more than the methods of synthetic geometry in a sort of Newtonian approach. All of our geometric constructions require straight edge and compass only.Comment: 9 pages, 4 figure

Relativistically extended Blanchard recurrence relation for hydrogenic matrix elements

General recurrence relations for arbitrary non-diagonal, radial hydrogenic matrix elements are derived in Dirac relativistic quantum mechanics. Our approach is based on a generalization of the second hypervirial method previously employed in the non-relativistic Schr\"odinger case. A relativistic version of the Pasternack-Sternheimer relation is thence obtained in the diagonal (i.e. total angular momentum and parity the same) case, from such relation an expression for the relativistic virial theorem is deduced. To contribute to the utility of the relations, explicit expressions for the radial matrix elements of functions of the form $r^\lambda$ and $\beta r^\lambda$ ---where $\beta$ is a Dirac matrix--- are presented.Comment: 21 pages, to be published in J. Phys. B: At. Mol. Opt. Phys. in Apri

Relativistic quantum mechanics of a Dirac oscillator

The Dirac oscillator is an exactly soluble model recently introduced in the context of many particle models in relativistic quantum mechanics. The model has been also considered as an interaction term for modelling quark confinement in quantum chromodynamics. These considerations should be enough for demonstrating that the Dirac oscillator can be an excellent example in relativistic quantum mechanics. In this paper we offer a solution to the problem and discuss some of its properties. We also discuss a physical picture for the Dirac oscillator's non-standard interaction, showing how it arises on describing the behaviour of a neutral particle carrying an anomalous magnetic moment and moving inside an uniformly charged sphere.Comment: 19 pages, 1 figur