Approximate relativistic bound states of a particle in Yukawa field with Coulomb tensor interaction

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 asymptotic 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.Comment: 16 pages. arXiv admin note: text overlap with arXiv:nucl-th/0411120 by other author

Bound states of spatially dependent mass Dirac equation with the Eckart potential including Coulomb tensor interaction

We investigate the approximate solutions of the Dirac equation with the position-dependent mass particle in the Eckart potential field including the Coulomb tensor interaction by using the parametric Nikiforov-Uvarov method. Taking an appropriate approximation to deal with the centrifugal term, the Dirac energy states and the corresponding normalized two-spinor components of the wave function are obtained in closed form. Some special cases of our solution are investigated. Furthermore, we present the correct solutions obtained via the asymptotic iteration method which are in agreement with the parametric Nikiforov-Uvarov method results.Comment: 24 pages, 1 figur

Approximate Analytical Solutions to Relativistic and Nonrelativistic P\"{o}schl-Teller Potential with its Thermodynamic Properties

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 pseudospin (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.Comment: 24 pages, 11 figure

Energy states of some diatomic molecules: Exact quantization rule approach

In this study, we obtain the approximate analytical solutions of the radial Schr\"{o}dinger equation for the Deng-Fan diatomic molecular potential by using exact quantization rule approach. The wave functions have been expressed by hypergeometric functions via the functional analysis approach. An extension to rotational-vibrational energy eigenvalues of some diatomic molecules are also presented. It is shown that the calculated energy levels are in good agreement with the ones obtained previously $E_{n\ell}-D$ (shifted Deng-Fan)

Dirac bound states of anharmonic oscillator in external fields

We explore the effect of the external magnetic and Aharonov-Bohm (AB) flux fields on the energy levels of Dirac particle subjects to mixed scalar and vector anharmonic oscillator field in the two-dimensional (2D) space. We calculate the exact energy eigenvalues and the corresponding un-normalized two-spinor-components wave functions in terms of the chemical potential parameter, magnetic field strength, AB flux field and magnetic quantum number by using the Nikiforov-Uvarov (NU) method

Formula Method for Bound State Problems

We present a simple formula for finding bound state solution of any quantum wave equation which can be simplified to the form of $\Psi"(s)+\frac{(k_1-k_2s)}{s(1-k_3s)}\Psi'(s)+\frac{(As^2+Bs+C)}{s^2(1-k_3s)^2}\Psi(s)=0$. The two cases where $k_3=0$ and $k_3\neq 0$ are studied. We derive an expression for the energy spectrum and the wave function in terms of generalized hypergeometric functions $_2F_1(\alpha, \beta; \gamma; k_3s)$. 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 been shown to be accurate, efficient, reliable and very easy to use particularly when applied to vast number of quantum potential models

Approximate bound state solutions of the deformed Woods-Saxon potential using asymptotic iteration method

By using the Pekeris approximation, the Schrodinger equation is approximately solved for the nuclear deformed Woods-Saxon potential within the framework of the asymptotic iteration method. The energy levels are worked out and the corresponding normalized eigenfunctions are obtained in terms of hypergeometric function.Comment: 14 pages, 10 figures; Chinese Physics Letters (2012

Spectroscopic study of some diatomic molecules via the proper quantization rule

Spectroscopic techniques are very essential tools in studying electronic structures, spectroscopic constants and energetic properties of diatomic molecules. These techniques are also required for parametrization of new method based on theoretical analysis and computational calculations. In this research, we apply the proper quantization rule in spectroscopic study of some diatomic molecules by solving the Schr\"odinger equation with two solvable quantum molecular systems-Tietz-Wei and shifted Deng-Fan potential models for their approximate nonrelativistic energy states via an appropriate approximation to the centrifugal term. We show that the energy levels can be determined from its ground state energy. The beauty and simplicity of the method applied in this study is that, it can be applied to any exactly as well as approximately solvable models. The validity and accuracy of the method is tested with previous techniques via numerical computation for H$_2$ and CO diatomic molecules. The result also include energy spectrum of 5 different electronic states of NO and 2 different electronic state of ICl.Comment: J. Math. Chem. (2015

Effect of oblateness, radiation and a circular cluster of material points on the stability of equilibrium points in the restricted four-body problem

Within the framework of restricted four-body problem, we study the motion of an infinitesimal mass by assuming that the primaries of the system are radiating-oblate spheroids surrounded by a circular cluster of material points. In our model, we assume that the two masses of the primaries $m_2$ and $m_3$ are equal to $\mu$ and the mass $m_1$ is $1-2\mu$. By using numerical approach, we have obtained the equilibrium points and examined their linear stability. The effect of potential created by the circular cluster and oblateness coefficients for the more massive primary and the less massive primary, on the existence and linear stability of the libration point have been critically examine via numerical computation. The stability of these points examined shows that the collinear and the non-collinear equilibrium points are unstable. The result presented in this paper have practical application in astrophysics.Comment: 13 pages, 2 figure

Analysis of quantum-mechanical states of the Mie-type ring shaped model via the Fisher's information entropy

In the recent years, information theory of quantum-mechanical systems have aroused the interest of many Theoretical Physicist. This due to the fact that it provides a deeper insight into the internal structure of the systems. Also, It is the strongest support of the modern quantum computation and information, which is basic for numerous technological developments. This study report the any $\ell-$state solution of the radial Schr\"{o}dinger equation with the Mie-type ring shaped diatomic molecular potential. Rotational-vibration of some few selected diatomic molecules are given. The probability distribution density of the system which gives the probability density for observing the electron in the state characterized by the quantum numbers $(n, l, m)$ in the Mie-type ring shaped diatomic molecular potential is obtained. Finally, we analyze this distribution via a complementary information measures of a probability distribution called as the Fisher's information entropy