Journal Title, Volume, Page:

Zeitschrift für Naturforschung A 01/2015; 70(2). DOI: 10.1515/zna-2014-0232
Year of Publication:

2015
Preferred Abstract (Original):

In this study, we obtain the approximate analytical solutions of the
radial Schrödinger equation for the Deng–Fan diatomic molecular
potential by using the exact quantisation rule approach. The wave
functions were expressed by hypergeometric functions via the functional
analysis approach. An extension to the rotational–vibrational energy
eigenvalues of some diatomic molecules is also presented. It is shown
that the calculated energy levels are in good agreement with those
obtained previously (*E*_{nℓ}–*D*; shifted Deng–Fan).

Year of Publication:

2014
Preferred Abstract (Original):

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 ℓ−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.
Journal Title, Volume, Page:

Physica Scripta ; 89(11):115204
Year of Publication:

2014
Preferred Abstract (Original):

In this study, approximate analytical solution of Schr\"odinger, 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 Schr\"odinger 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 analysed 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.

Journal Title, Volume, Page:

Journal of Molecular Structure: THEOCHEM Volume 855, Issues 1–3, Pages 13–17
Year of Publication:

2008
Preferred Abstract (Original):

The polynomial solution of the *D*-dimensional Schrödinger equation for a special case of Mie potential is obtained with an arbitrary *l*≠0 states. The exact bound state energies and their corresponding wave functions are calculated. The bound state (real) and positive (imaginary) cases are also investigated. In addition, we have simply obtained the results from the solution of the Coulomb potential by an appropriate transformation.

Journal Title, Volume, Page:

Journal of Molecular Structure: THEOCHEM 806, 155–158
Year of Publication:

2007
Preferred Abstract (Original):

The polynomial solution of the Schrodinger equation for the Pseudoharmonic potential is found for any arbitrary angular momentum
Journal Title, Volume, Page:

Molecular Physics Vol. 110, No. 24 , 3031–3039
Year of Publication:

2012
Preferred Abstract (Original):

The trigonometric P\"oschl-Teller (PT) potential describes the diatomic molecular vibration. We have obtained the approximate solutions of the radial Schr\"odinger equation (SE) for the rotating trigonometric PT potential using the Nikiforov-Uvarov (NU) method. The energy eigenvalues and their corresponding eigenfunctions are calculated for arbitrary -states in closed form. In the low screening region, when the screening parameter the potential reduces to Kratzer potential. Further, some numerical results are presented for several diatomic molecules.

Journal Title, Volume, Page:

Journal of Mathematical Chemistry, Volume 51, Issue 1, pp 227-238
Year of Publication:

2013
Preferred Abstract (Original):

We obtain the bound-state solutions of the radial Schrödinger equation with the shifted Deng–Fan oscillator potential in the frame of the Nikiforov-Uvarov method by employing Pekeris-type approximation to deal with the centrifugal term. The analytical expressions for the energy eigenvalues and the corresponding normalized wave functions are obtained in closed form for arbitrary *l*-state. The ro-vibrational energy levels for a few diatomic molecules are also calculated. They are found to be in good agreement with those ones previously obtained by the Morse potential.

Journal Title, Volume, Page:

Int J Theor Phys , 46: 2384–2395
Year of Publication:

2007
Preferred Abstract (Original):

We show that the exact energy eigenvalues and eigenfunctions of the Schrodinger equation for charged particles moving in certain class of non-central potentials can be easily calculated analytically in a simple and elegant manner by using Nikiforov and Uvarov (NU) method. We discuss the generalized Coulomb and harmonic oscillator systems. We study the Hartmann Coulomb and the ring-shaped and compound Coulomb plus Aharanov-Bohm potentials as special cases. The results are in exact agreement with other methods.

Journal Title, Volume, Page:

International Journal of Modern Physics E Vol. 21, No. 2 1250016 (13 pages)
Year of Publication:

2012
Preferred Abstract (Original):

We obtain analytical solutions of the two-body spinless Salpeter (SS) equation with Yukawa potential within the conventional approximation scheme to the centrifugal term for any -state. The semi-relativistic bound state energy spectra and the corresponding normalized wave functions are calculated by means of the Nikiforov-Uvarov (NU) method. We also obtain the numerical energy spectrum of the SS equation without any approximation to centrifugal term for the same potential and compare them with the approximated numerical ones obtained from the analytical expressions. It is found that the exact numerical results are in good agreement with the approximated ones for the lower energy states. Special cases are treated like the nonrelativistic limit and the solution for the Coulomb problem.

Journal Title, Volume, Page:

Chem. Phys., 421, 84-95
Year of Publication:

2013
Preferred Abstract (Original):

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.