123 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
Bound states of the Klein-Gordon equation for vector and scalar general Hulthen-type potentials in D-dimension
We solve the Klein-Gordon equation in any -dimension for the scalar and
vector general Hulth\'{e}n-type potentials with any by using an
approximation scheme for the centrifugal potential. Nikiforov-Uvarov method is
used in the calculations. We obtain the bound state energy eigenvalues and the
corresponding eigenfunctions of spin-zero particles in terms of Jacobi
polynomials. The eigenfunctions are physical and the energy eigenvalues are in
good agreement with those results obtained by other methods for D=1 and 3
dimensions. Our results are valid for value when and for any
value when and D=1 or 3. The % -wave () binding energies for
a particle of rest mass are calculated for the three lower-lying
states using pure vector and pure scalar potentials.Comment: 25 page
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
On the solutions of the Schrodinger equation with some molecular potentials: wave function ansatz
Making an ansatz to the wave function, the exact solutions of the %
-dimensional radial Schrodinger equation with some molecular potentials like
pseudoharmonic and modified Kratzer potentials are obtained. The restriction on
the parameters of the given potential, and are also given,
where depends on a linear combination of the angular momentum quantum
number and the spatial dimensions and is a parameter in
the ansatz to the wave function. On inserting D=3, we find that the bound state
eigensolutions recover their standard analytical forms in literature.Comment: 14 page
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
Any l-state solutions of the Woods-Saxon potential in arbitrary dimensions within the new improved quantization rule
The approximated energy eigenvalues and the corresponding eigenfunctions of
the spherical Woods-Saxon effective potential in dimensions are obtained
within the new improved quantization rule for all -states. The Pekeris
approximation is used to deal with the centrifugal term in the effective
Woods-Saxon potential. The inter-dimensional degeneracies for various orbital
quantum number and dimensional space are studied. The solutions for the
Hulth\'{e}n potential, the three-dimensional (D=3), the -wave () and
the cases are briefly discussed.Comment: 15 page
Exact solutions of the radial Schrodinger equation for some physical potentials
By using an ansatz for the eigenfunction, we have obtained the exact
analytical solutions of the radial Schrodinger equation for the pseudoharmonic
and Kratzer potentials in two dimensions. The energy levels of all the bound
states are easily calculated from this eigenfunction ansatz. The normalized
wavefunctions are also obtained.Comment: 13 page
Approximate analytical solutions of the generalized Woods-Saxon potentials including the spin-orbit coupling term and spin symmetry
We study the approximate analytical solutions of the Dirac equation for the
generalized Woods-Saxon potential with the pseudo-centrifugal term. In the
framework of the spin and pseudospin symmetry concept, the approximately
analytical bound state energy eigenvalues and the corresponding upper- and
lower-spinor components of the two Dirac particles are obtained, in closed
form, by means of the Nikiforov-Uvarov method which is based on solving the
second-order linear differential equation by reducing it to a generalized
equation of hypergeometric type. The special cases ( s-wave) and the non-relativistic limit can be reached easily
and directly for the generalized and standard Woods-Saxon potentials. Also, the
non-relativistic results are compared with the other works.Comment: 25 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
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