With the introduction of a new improved approximation scheme (Pekeris-type approximation) to deal with the centrifugal term, the energy eigenvalues and the wave functions of the Schrodinger equation of the shifted Deng-Fan molecular potential ¨ are obtained, via the asymptotic iteration method. Rotationalvibrational energy eigenvalues of some diatomic molecules are presented, these results are in good agreement with other results in the literature. For these selected diatomic molecules, energy eigenvalues obtained are in much better agreement with the results obtained from the rotating Morse potential model for moderate values of rotational and vibrational quantum numbers. Furthermore, thermodynamic properties such as the vibrational mean U, specific heat C, free energy F and entropy S for the pure vibrational state in the classical limit for these energy eigenvalues are studied.

By using the wave function ansatz method, we study the energy eigenvalues and wave function for any arbitrary m-state in two-dimensional Schrödinger wave equation with various power interaction potentials in constant magnetic and Aharonov-Bohm (AB) 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 = 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.1 describing the molecular vibrations is important in studying the dynamical variables of diatomic molecules [3]. This potential have a wide applications in various fields of physics and chemistry such as molecular physics, solid-state physics, chemical physics, quantum chemistry, the molecular dynamics study of linear diatomic molecules and the theoretical works on the spectral properties of a diatomic molecule system [4]. Therefore, we found that it is necessary to study the exact bound state solutions of the two-dimensional (2D) solution of the Schrödinger equation for these potentials under the influence of external magnetic and Aharonov-Bohm fields. The 2D hydrogen model was treated as an atomic spectroscopy and used as a simplified model of the ionization process of the highly excited 3D hydrogen atom by circular-polarized microwaves [5]. The field-free relativistic Coulomb interaction has been studied by many authors by using various techniques [6, 7, 8]. The nonrelativistic H-like atom under the influence of magnetic field has been the subject of study over the past years [9, 10, 11]. In the presence of a low magnetic field, the quasi-classical solution of the Dirac equation has been obtained by factorization method [12]. In the framework of the variational method, the ground-state Dirac energies and relativistic spinless lowest few states have been calculated for arbitrary strength values of magnetic field [13, 14, 15]. The Klein-Gordon wave equation was solved exactly for particular values of magnetic field in which the wave function can be expressed in closed analytical form [16]. The polynomial solutions of the Schrödinger equation was obtained for the ground-state and a few first excited states of 2D hydrogenic atoms for particular values of the magnetic field strength perpendicular to the plane of transversal motion of the electron using a relativistic wave function [17]. Recently, within the framework of power-series solutions, the Klein-Gordon and Dirac equations have beensolved for the 2D hydrogen-like systems when an arbitrary external magnetic field is applied [18]. For particular values of magnetic field B, it is found that the exact ...

We present a simple formula for finding bound state solution of any quantum wave equation which can be simplified to the form of Ψ ′′ (s)The two cases where k 3 = 0 and k 3 = 0 are studied. We derive an expression for the energy spectrum and the wave function in terms of generalized hypergeometric functions 2 F 1 (α, β; γ; k 3 s). 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 shown to be accurate, efficient, reliable and very easy to use particularly when applied to vast number of quantum potential models.

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In this study, approximate analytical solution of Schrödinger, Klein-Gordon and Dirac equations under the Tietz-Wei (TW) diatomic molecular potential are represented by using an approximation for the centrifugal term. We have applied three types of eigensolution techniques; the functional analysis approach (FAA), supersymmetry quantum mechanics (SUSYQM) and asymptotic iteration method (AIM) to solve Klein-Gordon, Dirac and Schrödinger equations, respectively. The energy eigenvalues and the corresponding eigenfunctions for these three wave equations are obtained and some numerical results and figures are reported. It has been shown that these techniques yielded exactly same results. some expectation values of the TW diatomic molecular potential within the framework of the Hellmann-Feynman theorem (HFT) have been presented. The probability distributions which characterize the quantum-mechanical states of TW diatomic molecular potential are analyzed by means of complementary information measures of a probability distribution called the Fishers information entropy. This distribution has been described in terms of Jacobi polynomials, whose characteristics are controlled by the quantum numbers.

Using the asymptotic iteration method (AIM), we have obtained analytical approximations to the ℓ-wave solutions of the Schrödinger equation with the Manning-Rosen potential. The equation of energy eigenvalues equation and the corresponding wavefunctions have been obtained explicitly. Three different Pekeris-type approximation schemes have been used to deal with the centrifugal term. To show the accuracy of our results, we have calculated the eigenvalues numerically for arbitrary quantum numbers n and ℓ for some diatomic molecules (HCl, CH, LiH and CO). It is found that the results are in good agreement with other results found in the literature. A straightforward extension to the s-wave case and Hulthén potential case are also presented.

We apply the asymptotic iteration method (AIM) to obtain the solutions of Schrödinger equation in the presence of Pöschl-Teller (PT) potential. We also obtain the solutions of Dirac equation for the same potential under the condition of spin and pseudospin (p-spin) symmetries. We show that in the nonrelativistic limits, the solution of Dirac system converges to that of Schrödinger 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.

By using the Pekeris approximation, the Schrödinger 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. The deformed Woods-Saxon (dWS) potential is a short range potential and widely used in nuclear, particle, atomic, condensed matter and chemical physics [1][2][3][4][5][6][7]. This potential is reasonable for nuclear shell models and used to represent the distribution of nuclear densities.The dWS and spin-orbit interaction are important and applicable to deformed nuclei [8] and to strongly deformed nuclides [9]. The dWS potential parameterization at large deformations for plutonium 237,239,241 P u odd isotopes was analyzed [10]. The structure of single-particle states in