Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userResonant states and pseudospin symmetry in the Dirac Morse potential
149
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
The complex scaling method is applied to study the resonances of a Dirac particle in a Morse potential. The applicability of the method is demonstrated with the results compared with the available data. It is shown that the present calculations in the nonrelativistic limit are in excellent agreement with the nonrelativistic calculations. Further, the dependence of the resonant parameters on the shape of the potential is checked, and the unusual sensitivity to the potential parameters is revealed. By comparing the energies and widths of the pseudospin doublets, well pseudospin symmetry is discovered in the present model. The relationship between the pseudospin symmetry and the shape of the potential is investigated by changing the Morse potential shaped by the dissociation energy, the equilibrium intermolecular distance, and the positive number controlling the decay length of the potential.
rate research
Read More
In this paper we construct coherent states for the two-dimensional Morse potential. We find the dependence of the spectrum on the physical parameters and use this to understand the emergence of accidental degeneracies. It is observed that, under certain conditions pertaining to the irrationality of the parameters, accidental degeneracies do not appear and as such energy levels are at most two-fold degenerate. After defining a non-degenerate spectrum and set of states for the 2D Morse potential, we construct generalised coherent states and discuss the spatial distribution of their probability densities and their uncertainty relations.
Supersymmetry is a technique that allows us to extract information about the states and spectra of quantum mechanical systems which may otherwise be unsolvable. In this paper we reconstruct Ioffes set of states for the singular non-separable two-dimensional Morse potential using supersymmetry from a non-degenerate set of states constructed for the initial separable Morse Hamiltonian. We define generalised coherent states, compute their uncertainty relations, and we find that the singularity in the partner Hamiltonian significantly affects the localisation of the coherent state wavefunction.
In the 70s Smith and Tassie, and Bell and Ruegg independently found SU(2) symmetries of the Dirac equation with scalar and vector potentials. These symmetries, known as pseudospin and spin symmetries, have been extensively researched and applied to several physical systems. Twenty years after, in 1997, the pseudospin symmetry has been revealed by Ginocchio as a relativistic symmetry of the atomic nuclei when it is described by relativistic mean field hadronic models. The main feature of these symmetries is the suppression of the spin-orbit coupling either in the upper or lower components of the Dirac spinor, thereby turning the respective second-order equations into Schrodinger-like equations, i.e, without a matrix structure. In this paper we propose a generalization of these SU(2) symmetries for potentials in the Dirac equation with several Lorentz structures, which also allow for the suppression of the matrix structure of second-order equation equation of either the upper or lower components of the Dirac spinor. We derive the general properties of those potentials and list some possible candidates, which include the usual spin-pseudospin potentials, and also 2- and 1-dimensional potentials. An application for a particular physical system in two dimensions, electrons in graphene, is suggested.
The Dirac-Morse problem are investigated within the framework of an approximation to the term proportional to $1/r^2$ in the view of the position-dependent mass formalism. The energy eigenvalues and corresponding wave functions are obtained by using the parametric generalization of the Nikiforov-Uvarov method for any $kappa$-value. It is also studied the approximate energy eigenvalues, and corresponding wave functions in the case of the constant-mass for pseudospin, and spin cases, respectively.
Light-induced control of ions within small Coulomb crystals is investigated. By intense intracavity optical standing wave fields, subwavelength localization of individual ions is achieved for one-, two-, and three-dimensional crystals. Based on these findings, we illustrate numerically how the application of such optical potentials can be used to tailor the normal mode spectra and patterns of multi-dimensional Coulomb crystals. The results represent, among others, important steps towards controlling the crystalline structure of Coulomb crystals, investigating heat transfer processes at the quantum limit and quantum simulations of many-body systems.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
