19 research outputs found
Exactly solvable effective mass D-dimensional Schrodinger equation for pseudoharmonic and modified Kratzer problems
We employ the point canonical transformation (PCT) to solve the D-dimensional
Schr\"{o}dinger equation with position-dependent effective mass (PDEM) function
for two molecular pseudoharmonic and modified Kratzer (Mie-type) potentials. In
mapping the transformed exactly solvable D-dimensional ()
Schr\"{o}dinger equation with constant mass into the effective mass equation by
employing a proper transformation, the exact bound state solutions including
the energy eigenvalues and corresponding wave functions are derived. The
well-known pseudoharmonic and modified Kratzer exact eigenstates of various
dimensionality is manifested.Comment: 13 page
New exact solution of the one dimensional Dirac Equation for the Woods-Saxon potential within the effective mass case
We study the one-dimensional Dirac equation in the framework of a position
dependent mass under the action of a Woods-Saxon external potential. We find
that constraining appropriately the mass function it is possible to obtain a
solution of the problem in terms of the hypergeometric function. The mass
function for which this turns out to be possible is continuous. In particular
we study the scattering problem and derive exact expressions for the reflection
and transmission coefficients which are compared to those of the constant mass
case. For the very same mass function the bound state problem is also solved,
providing a transcendental equation for the energy eigenvalues which is solved
numerically.Comment: Version to match the one which has been accepted for publication by
J. Phys. A: Math. Theor. Added one figure, several comments and few
references. (24 pages and 7 figures
Any l-state improved quasi-exact analytical solutions of the spatially dependent mass Klein-Gordon equation for the scalar and vector Hulthen potentials
We present a new approximation scheme for the centrifugal term to obtain a
quasi-exact analytical bound state solutions within the framework of the
position-dependent effective mass radial Klein-Gordon equation with the scalar
and vector Hulth\'{e}n potentials in any arbitrary dimension and orbital
angular momentum quantum numbers The Nikiforov-Uvarov (NU) method is used
in the calculations. The relativistic real energy levels and corresponding
eigenfunctions for the bound states with different screening parameters have
been given in a closed form. It is found that the solutions in the case of
constant mass and in the case of s-wave () are identical with the ones
obtained in literature.Comment: 25 pages, 1 figur
Calculation of the B_{c}leptonic decay constant using the shifted N-expansion method
We give a review and present a comprehensive calculation for the leptonic
constant B_{c} of the low-lying pseudoscalar and vector states of B_{c}-meson
in the framework of static and QCD-motivated nonrelativistic potential models
taking into account the one-loop and two-loop QCD corrections in the short
distance coefficient that governs the leptonic constant of quarkonium
system. Further, we use the scaling relation to predict the leptonic constant
of the nS-states of the (b_bar)c system. Our results are compared with other
models to gauge the reliability of the predictions and point out differences.Comment: 26 page
Non-relativistic quark-antiquark potential: spectroscopy of heavy-quarkonia and exotic SUSY quarkonia
The experiments at LHC have shown that the SUSY (exotic) bound states are
likely to form bound states in an entirely similar fashion as ordinary quarks
form bound states, i.e., quarkonium. Also, the interaction between two squarks
is due to gluon exchange which is found to be very similar to that interaction
between two ordinary quarks. This motivates us to solve the Schr\"{o}dinger
equation with a strictly phenomenological static quark-antiquark potential:
using the shifted large -expansion
method to calculate the low-lying spectrum of a heavy quark with
anti-sbottom\textbf{\} and
sbottom with anti-sbottom bound states
with is set free. To have a full knowledge on spectrum, we
also give the result for a heavier as well as for lighter sbottom masses. As a
test for the reliability of these calculations, we fix the parameters of this
potential by fitting the spin-triplet and center-of-gravity
experimental spectrum of the ordinary heavy quarkonia
and to few Our results are
compared with other models to gauge the reliability of these predictions and
point out differences.Comment: 30 page
A General Approach for the Exact Solution of the Schrodinger Equation
The Schr\"{o}dinger equation is solved exactly for some well known
potentials. Solutions are obtained reducing the Schr\"{o}dinger equation into a
second order differential equation by using an appropriate coordinate
transformation. The Nikiforov-Uvarov method is used in the calculations to get
energy eigenvalues and the corresponding wave functions.Comment: 20 page
Bound-States of the Spinless Salpeter Equation for the PT-Symmetric Generalized Hulthen Potential by the Nikiforov-Uvarov Method
The one-dimensional spinless Salpeter equation has been solved for the
PT-symmetric generalized Hulth\'{e}n potential. The Nikiforov-Uvarov {NU)
method which is based on solving the second-order linear differential equations
by reduction to a generalized equation of hypergeometric type is used to obtain
exact energy eigenvalues and corresponding eigenfunctions. We have investigated
the positive and negative exact bound states of the s-states for different
types of complex generalized Hulthen potentials.Comment: 24 page
Analytical Solutions of Klein-Gordon Equation with Position-Dependent Mass for q-Parameter Poschl-Teller potential
The energy eigenvalues and the corresponding eigenfunctions of the
one-dimensional Klein-Gordon equation with q-parameter Poschl-Teller potential
are analytically obtained within the position-dependent mass formalism. The
parametric generalization of the Nikiforov-Uvarov method is used in the
calculations by choosing a mass distribution.Comment: 10 page
Any -state solutions of the Hulth\'en potential by the asymptotic iteration method
In this article, we present the analytical solution of the radial
Schr\"{o}dinger equation for the Hulth\'{e}n potential within the framework of
the asymptotic iteration method by using an approximation to the centrifugal
potential for any states. We obtain the energy eigenvalues and the
corresponding eigenfunctions for different screening parameters. The wave
functions are physical and energy eigenvalues are in good agreement with the
results obtained by other methods for different values. In order to
demonstrate this, the results of the asymptotic iteration method are compared
with the results of the supersymmetry, the numerical integration, the
variational and the shifted 1/N expansion methods.Comment: 14 pages and 1 figur