By using the wave function ansatz method, we study the energy eigenvalues and wave function for any arbitrary $m$-state in two-dimensional Schr{o}dinger wave equation with various power interaction potentials in constant magnetic and Aharonov-Bohm (A
B) 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 $m eq 0$ and its influence on $m=0$ 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.
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 pseu
dospin (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.
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 as
ymptotic 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.
Approximate bound state solutions of the Dirac equation with -deformed Woods-Saxon plus a new generalized ring-shaped potential are obtained for any arbitrary L-state. The energy eigenvalue equation and corresponding two-component wave function are c
alculated by solving the radial and angular wave equations within a shortcut of the Nikiforov-Uvarov method. The solutions of the radial and polar angular parts of the wave function are expressed in terms of the Jacobi polynomials. A new approximation being expressed in terms of the potential parameters is carried out to deal with the strong singular centrifugal potential term L(L+1)/r^2. Under some limitations, we can obtain solution for the ring-shaped Hulthen potential and the standard usual spherical Woods-Saxon potential (q=1).
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 e
igenfunctions are obtained in terms of hypergeometric function.
Approximate bound state solutions of the Dirac equation with the Hulthen plus a new generalized ring-shaped (RS) potential are obtained for any arbitrary -state. The energy eigenvalue equation and the corresponding two-component wave function are cal
culated by solving the radial and angular wave equations within a recently introduced shortcut of Nikiforov-Uvarov (NU) method. The solutions of the radial and polar angular parts of the wave function are given in terms of the Jacobi polynomials. We use an exponential approximation in terms of the Hulthen potential parameters to deal with the strong singular centrifugal potential term Under the limiting case, the solution can be easily reduced to the solution of the Schrodinger equation with a new ring-shaped Hulthen potential.
The Duffin Kemmer Petiau (DKP) equation is solved approximately for a vector exponential-like decaying potential with any arbitrary J state by using the Pekeris approximation. The generalized parametric Nikiforov-Uvarov (NU) method is used to obtain
energy eigenvalues and corresponding wave functions in a closed form. The cases of zero total angular momentum and nonrelativistic limit are discussed too.
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 pseud
ospin (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 Schrodinger solutions for Yukawa and inversely quadratic Yukawa potentials.
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 t
o 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 $% s$-wave ($l=0$) and the cases are briefly discussed.
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 o
btain 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 $l eq 0$ 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.
