47 research outputs found
Relativistic symmetries in Rosen-Morse potential and tensor interaction using the Nikiforov-Uvarov method
Approximate analytical bound-state solutions of the Dirac particle in the
field of both attractive and repulsive RM potentials including Coulomb-like
tensor (CLT) potential are obtained for arbitrary spin-orbit quantum number The
Pekeris approximation is used to deal with the spin-orbit coupling terms In the
presence of exact spin and pseudospin (p-spin) symmetries, the energy
eigenvalues and the corresponding normalized two-component wave functions are
found by using the parametric generalization of the Nikiforov-Uvarov (NU)
method. The numerical results show that the CLT interaction removes
degeneracies between spin and p-spin state doublets.Comment: 16 pages ; 4 figure
Approximate Dirac solutions of complex -symmetric P\"oschl-Teller potential in view of spin and pseudospin symmetries
By employing an exponential-type approximation scheme to replace the
centrifugal term, we have approximately solved the Dirac equation for spin-
particle subject to the complex -symmetric scalar and vector P\"oschl-Teller
(PT) potentials with arbitrary spin-orbit -wave states in view of spin and
pseudospin (p-spin) symmetries. The real bound-state energy eigenvalue equation
and the corresponding two-spinor components wave function expressible in terms
of the hypergeometric functions are obtained by means of the wave function
analysis. The spin- Dirac equation and the spin- Klein-Gordon (KG) equation
with the complex P\"oschl-Teller potentials share the same energy spectrum
under the choice of (i.e., exact spin and p-spin symmetries).Comment: 22 pages; 10 figures, to appear in Physica Scripta (2012
Spinless particles with unequal Scalar-Vector Yukawa interactions
We present analytical solutions of the spin-zero Klein-Gordon (KG) bosons in
the field of unequal mixture of scalar and vector Yukawa potential within the
framework of the approximation to the centrifugal potential term for any
arbitrary -state. The explicit forms of the energy bound states including
energy spectra and unnormalized wave functions are obtained using a simple
shortcut of the Nikiforov-Uvarov (NU) method. Our numerical tests using energy
calculations demonstrate the existence of inter dimensional degeneracy amongst
energy states of the present quantum system consisting of the KG-Yukawa
problem. The dependence of the energy on the dimension is numerically discussed
forComment: 13 pages; 1 figures; Chinese Physics B (2012
Relativistic new Yukawa-like potential and tensor coupling
We approximately solve the Dirac equation for a new suggested generalized
inversely quadratic Yukawa (GIQY) potential including a Coulomb-like tensor
interaction with arbitrary spin-orbit coupling quantum number In the framework
of the spin and pseudospin (p-spin) symmetry, we obtain the energy eigenvalue
equation and the corresponding eigenfunctions, in closed form, by using the
parametric Nikiforov-Uvarov (NU) method. The numerical results show that the
Coulomb-like tensor interaction, removes degeneracies between spin and p-spin
state doublets. The Dirac solutions in the presence of exact spin symmetry are
reduced to Schr\"odinger solutions for Yukawa and inversely quadratic Yukawa
potentials.Comment: 22 pages, 1 figure. arXiv admin note: substantial text overlap with
arXiv:1203.676
Effects of external fields on two-dimensional Klein-Gordon particle under pseudoharmonic oscillator interaction
We study the effects of the perpendicular magnetic and Aharonov-Bohm (AB)
flux fields on the energy levels of a two-dimensional (2D) Klein-Gordon (KG)
particle subjects to equal scalar and vector pseudo-harmonic oscillator (PHO).
We calculate the exact energy eigenvalues and normalized wave functions in
terms of chemical potential parameter, magnetic field strength, AB flux field
and magnetic quantum number by means of the Nikiforov-Uvarov (NU) method. The
non-relativistic limit, PHO and harmonic oscillator solutions in the existence
and absence of external fields are also obtained.Comment: 13 pages, to appear in Chinese Physics B (2012). arXiv admin note:
text overlap with arXiv:hep-th/050320
Effect of Tensor Interaction in the Dirac-Attractive Radial Problem under Pseudospin Symmetry limit
We approximately investigated pseudospin symmetric solutions of the Dirac
equation for attractive radial potential including a Coulomb-like tensor
interaction under pseudospin symmetry limit for any spin-orbit quantum number .
By using the parametric generalization of the Nikiforov-Uvarov method, the
energy eigenvalues equation and the corresponding wave functions have been
obtained in closed forms. Some numerical results are also given. We presented
tensor interaction removes degeneracy between two states in pseudospin
doublets.Comment: 13 pages, 2 figure
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
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 eigensolutions of the deformed Woods-Saxon potential via AIM
By using the Pekeris approximation, the Schr\"{o}dinger equation is solved
for the nuclear deformed Woods-Saxon potential within the framework of the
asymptotic iteration method (AIM). The energy levels are worked out and the
corresponding normalized eigenfunctions are obtained in terms of hypergeometric
function.Comment: 14 pages, 8 figures. arXiv admin note: substantial text overlap with
arXiv:1207.121