188 research outputs found
Supersymmetry and superalgebra for the two-body system with a Dirac oscillator interaction
Some years ago, one of the authors~(MM) revived a concept to which he gave
the name of single-particle Dirac oscillator, while another~(CQ) showed that it
corresponds to a realization of supersymmetric quantum mechanics. The Dirac
oscillator in its one- and many-body versions has had a great number of
applications. Recently, it included the analytic expression for the eigenstates
and eigenvalues of a two-particle system with a new type of Dirac oscillator
interaction of frequency~. By considering the latter together with its
partner corresponding to the replacement of~ by~, we are able
to get a supersymmetric formulation of the problem and find the superalgebra
that explains its degeneracy.Comment: 21 pages, LaTeX, 1 figure (can be obtained from the authors), to
appear in J. Phys.
Relativistic echo dynamics and the stability of a beam of Landau electrons
We extend the concepts of echo dynamics and fidelity decay to relativistic
quantum mechanics, specifically in the context of Klein-Gordon and Dirac
equations under external electromagnetic fields. In both cases we define
similar expressions for the fidelity amplitude under perturbations of these
fields, and a covariant version of the echo operator. Transformation properties
under the Lorentz group are established. An alternate expression for fidelity
is given in the Dirac case in terms of a 4-current. As an application we study
a beam of Landau electrons perturbed by field inhomogeneities.Comment: 8 pages, no figure
New hydrogen-like potentials
Using the modified factorization method introduced by Mielnik, we construct a
new class of radial potentials whose spectrum for l=0 coincides exactly with
that of the hydrogen atom. A limiting case of our family coincides with the
potentials previously derived by Abraham and MosesComment: 6 pages, latex, 2 Postscript figure
Six-dimensional Davidson potential as a dynamical symmetry of the symplectic Interacting Vector Boson Model
A six-dimensional Davidson potential, introduced within the framework of the
Interacting Vector Boson Model (IVBM), is used to describe nuclei that exhibit
transitional spectra between the purely rotational and vibrational limits of
the theory. The results are shown to relate to a new dynamical symmetry that
starts with the reduction. Exact
solutions for the eigenstates of the model Hamiltonian in the basis defined by
a convenient subgroup chain of SO(6) are obtained. A comparison of the
theoretical results with experimental data for heavy nuclei with transitional
spectra illustrates the applicability of the theory.Comment: 9 pages, 4 figure
Solution of One-dimensional Dirac Equation via Poincare Map
We solve the general one-dimensional Dirac equation using a "Poincare Map"
approach which avoids any approximation to the spacial derivatives and reduces
the problem to a simple recursive relation which is very practical from the
numerical implementation point of view. To test the efficiency and rapid
convergence of this approach we apply it to a vector coupling Woods--Saxon
potential, which is exactly solvable. Comparison with available analytical
results is impressive and hence validates the accuracy and efficiency of this
method.Comment: 8 pages, 6 figures. Version to appear in EP
The Dirac-Dowker Oscillator
The oscillator-like interaction is introduced in the equation for the
particle of arbitrary spin, given by Dirac and re-written to a matrix form by
Dowker.Comment: LaTeX file, 4pp. Preprint EFUAZ 94-0
Comment on ``the Klein-Gordon Oscillator''
The different ways of description of the particle with oscillator-like
interaction are considered. The results are in conformity with the previous
paper of S. Bruce and P. Minning.Comment: LaTeX file, 5p
Relativistic shape invariant potentials
Dirac equation for a charged spinor in electromagnetic field is written for
special cases of spherically symmetric potentials. This facilitates the
introduction of relativistic extensions of shape invariant potential classes.
We obtain the relativistic spectra and spinor wavefunctions for all potentials
in one of these classes. The nonrelativistic limit reproduces the usual
Rosen-Morse I & II, Eckart, Poschl-Teller, and Scarf potentials.Comment: Corrigendum: The last statement above equation (1) is now corrected
and replaced by two new statement
Energy spectrum of the relativistic Dirac-Morse problem
We derive an elegant analytic formula for the energy spectrum of the
relativistic Dirac-Morse problem, which has been solved recently. The new
formula displays the properties of the spectrum more vividly.Comment: Replaced with a more potrable PDF versio
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