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 ($D\geq 2$) 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 $D$-dimension for the scalar and vector general Hulth\'{e}n-type potentials with any $l$ 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 $q=1$ value when $l\neq 0$ and for any $q$ value when $l=0$ and D=1 or 3. The $s$% -wave ($l=0$) binding energies for a particle of rest mass $m_{0}=1$ are calculated for the three lower-lying states $(n=0,1,2)$ 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 $B_{c}$ 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 $D$% -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, $\delta$ and $\eta$ are also given, where $\eta$ depends on a linear combination of the angular momentum quantum number $\ell$ and the spatial dimensions $D$ and $\delta$ 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 $D$ dimension and orbital angular momentum quantum numbers $l.$ 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 ($l=0$) 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 $D$ dimensions are obtained within the new improved quantization rule for all $l$-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 $l$ and dimensional space $D$ are studied. The solutions for the Hulth\'{e}n potential, the three-dimensional (D=3), the $$-wave ($l=0$) 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 $\kappa =\pm 1$ ($l=\widetilde{l}=0,$ 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