82 research outputs found
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 and the
terms ( is a Dirac matrix and 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
Limitations on the superposition principle: superselection rules in non-relativistic quantum mechanics
The superposition principle is a very basic ingredient of quantum theory.
What may come as a surprise to many students, and even to many practitioners of
the quantum craft, is tha superposition has limitations imposed by certain
requirements of the theory. The discussion of such limitations arising from the
so-called superselection rules is the main purpose of this paper. Some of their
principal consequences are also discussed. The univalence, mass and particle
number superselection rules of non-relativistic quantum mechanics are also
derived using rather simple methods.Comment: 22 pages, no 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 and
---where is a Dirac matrix--- are presented.Comment: 21 pages, to be published in J. Phys. B: At. Mol. Opt. Phys. in Apri
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
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
- âŠ