18 research outputs found
Approximate relativistic bound states of a particle in Yukawa field with Coulomb tensor interaction
We obtain the approximate relativistic bound state of a spin-1/2 particle in
the field of the Yukawa potential and a Coulomb-like tensor interaction with
arbitrary spin-orbit coupling number k under the spin and pseudospin (p-spin)
symmetries. The asymptotic iteration method is used to obtain energy
eigenvalues and corresponding wave functions in their closed forms. Our
numerical results show that the tensor interaction removes degeneracies between
the spin and p-spin doublets and creates new degenerate doublets for various
strengths of tensor coupling.Comment: 16 pages. arXiv admin note: text overlap with arXiv:nucl-th/0411120
by other author
Approximate Analytical Solutions to Relativistic and Nonrelativistic P\"{o}schl-Teller Potential with its Thermodynamic Properties
We apply the asymptotic iteration method (AIM) to obtain the solutions of
Schrodinger equation in the presence of Poschl-Teller (PT) potential. We also
obtain the solutions of Dirac equation for the same potential under the
condition of spin and pseudospin (p-spin) symmetries. We show that in the
nonrelativistic limits, the solution of Dirac system converges to that of
Schrodinger system. Rotational-Vibrational energy eigenvalues of some diatomic
molecules are calculated. Some special cases of interest are studied such as
s-wave case, reflectionless-type potential and symmetric hyperbolic PT
potential. Furthermore, we present a high temperature partition function in
order to study the behavior of the thermodynamic functions such as the
vibrational mean energy U, specific heat C, free energy F and entropy S.Comment: 24 pages, 11 figure
Effect of oblateness, radiation and a circular cluster of material points on the stability of equilibrium points in the restricted four-body problem
Within the framework of restricted four-body problem, we study the motion of
an infinitesimal mass by assuming that the primaries of the system are
radiating-oblate spheroids surrounded by a circular cluster of material points.
In our model, we assume that the two masses of the primaries and
are equal to and the mass is . By using numerical approach,
we have obtained the equilibrium points and examined their linear stability.
The effect of potential created by the circular cluster and oblateness
coefficients for the more massive primary and the less massive primary, on the
existence and linear stability of the libration point have been critically
examine via numerical computation. The stability of these points examined shows
that the collinear and the non-collinear equilibrium points are unstable. The
result presented in this paper have practical application in astrophysics.Comment: 13 pages, 2 figure
Energy states of some diatomic molecules: Exact quantization rule approach
In this study, we obtain the approximate analytical solutions of the radial
Schr\"{o}dinger equation for the Deng-Fan diatomic molecular potential by using
exact quantization rule approach. The wave functions have been expressed by
hypergeometric functions via the functional analysis approach. An extension to
rotational-vibrational energy eigenvalues of some diatomic molecules are also
presented. It is shown that the calculated energy levels are in good agreement
with the ones obtained previously (shifted Deng-Fan)
Dirac bound states of anharmonic oscillator in external fields
We explore the effect of the external magnetic and Aharonov-Bohm (AB) flux
fields on the energy levels of Dirac particle subjects to mixed scalar and
vector anharmonic oscillator field in the two-dimensional (2D) space. We
calculate the exact energy eigenvalues and the corresponding un-normalized
two-spinor-components wave functions in terms of the chemical potential
parameter, magnetic field strength, AB flux field and magnetic quantum number
by using the Nikiforov-Uvarov (NU) method
Formula Method for Bound State Problems
We present a simple formula for finding bound state solution of any quantum
wave equation which can be simplified to the form of
.
The two cases where and are studied. We derive an
expression for the energy spectrum and the wave function in terms of
generalized hypergeometric functions . In
order to show the accuracy of this proposed formula, we resort to obtaining
bound state solutions for some existing eigenvalue problems in a rather more
simplified way. This method has been shown to be accurate, efficient, reliable
and very easy to use particularly when applied to vast number of quantum
potential models
Spectroscopic study of some diatomic molecules via the proper quantization rule
Spectroscopic techniques are very essential tools in studying electronic
structures, spectroscopic constants and energetic properties of diatomic
molecules. These techniques are also required for parametrization of new method
based on theoretical analysis and computational calculations. In this research,
we apply the proper quantization rule in spectroscopic study of some diatomic
molecules by solving the Schr\"odinger equation with two solvable quantum
molecular systems-Tietz-Wei and shifted Deng-Fan potential models for their
approximate nonrelativistic energy states via an appropriate approximation to
the centrifugal term. We show that the energy levels can be determined from its
ground state energy. The beauty and simplicity of the method applied in this
study is that, it can be applied to any exactly as well as approximately
solvable models. The validity and accuracy of the method is tested with
previous techniques via numerical computation for H and CO diatomic
molecules. The result also include energy spectrum of 5 different electronic
states of NO and 2 different electronic state of ICl.Comment: J. Math. Chem. (2015
Approximate bound state solutions of the deformed Woods-Saxon potential using asymptotic iteration method
By using the Pekeris approximation, the Schrodinger equation is approximately
solved for the nuclear deformed Woods-Saxon potential within the framework of
the asymptotic iteration method. The energy levels are worked out and the
corresponding normalized eigenfunctions are obtained in terms of hypergeometric
function.Comment: 14 pages, 10 figures; Chinese Physics Letters (2012
Comment on "Analytic model of the energy spectrum of a graphene quantum dot in a perpendicular magnetic field"
In recent work by Schnez et al. [PRB 78, 195427 (2008)], they studied the
analytical model of the energy spectrum of a graphene quantum dot in a
perpendicular magnetic field. In this comment we first point out that the
results Eqs.(5), (6) and (11) presented by them in [1] are not reliable and
then give our results
Nonrelativistic molecular models under external magnetic and AB flux fields
By using the wave function ansatz method, we study the energy eigenvalues and
wave function for any arbitrary -state in two-dimensional Schr\"{o}dinger
wave equation with various power interaction potentials in constant magnetic
and Aharonov-Bohm (AB) flux fields perpendicular to the plane where the
interacting particles are confined. We calculate the energy levels of some
diatomic molecules in the presence and absence of external magnetic and AB flux
fields using different potential models. We found that the effect of the
Aharonov-Bohm field is much as it creates a wider shift for and its
influence on states is found to be greater than that of the magnetic
field. To show the accuracy of the present model, a comparison is made with
those ones obtained in the absence of external fields. An extension to
3-dimensional quantum system have also been presented