Nonrelativistic Studies of Diatomic Molecules of Schrödinger Particles with Yukawa Plus Ring-Shaped Potential Model (original) (raw)

Yukawa-angle Dependent Potential and its Applications to Diatomic Molecules under Schrodinger wave Equation

Journal of Applied and Theoretical Physics Research

In this paper, we have solved the Schrödinger wave equation with Yukawa plus novel angle dependent potential using powerful Nikiforov-Uvarov method and obtained the energy eigenvalues and corresponding wave functions in terms of Jacobi and Laguerre polynomials for the angular and radial part respectively. We have also presented the effect of angle dependent solution on radial solutions and also applied our results to obtain numerical values for some selected diatomic molecules. We also studied the behavior of our potential graphically for H 2 diatomic molecule.

Approximate analytic solutions of the diatomic molecules in the Schrodinger equation with hyperbolical potentials

2009

The Schrodinger equation for the rotational-vibrational (ro-vibrational) motion of a diatomic molecule with empirical potential functions is solved approximately by means of the Nikiforov-Uvarov method. The approximate ro-vibratinal energy spectra and the corresponding normalized total wavefunctions are calculated in closed form and expressed in terms of the hypergeometric functions or Jacobi polynomials P_n^(μ,ν)(x), where μ>-1, ν>-1 and x included in [-1,+1]. The s-waves analytic solution is obtained. The numerical energy eigenvalues for selected H_2 and Ar_2 molecules are also calculated and compared with the previous models and experiments.

Solutions of the Schrodinger Equation with Inversely Quadratic Yukawa plus attractive radial Potential using Nikiforov-Uvarov method

In this paper, we have solved the Schrodinger equation with a new superposed potential (IQYARP) made of inversely quadratic Yukawa potential and attractive radial potential using the parametric Nikiforov-Uvarov (NU) method. The solutions of the Schrodinger equation enabled us to obtainbound state energy eigenvalues and their corresponding un-normalized eigen functions in terms of Jacobi polynomials. Also, a special case of the potential has been considered and its energy eigen values obtained. Our calculation reveals bound state energy eigenvalues which can be applied to molecules moving under the influence of IQYARP potential.

Evaluation of the bound state energies of some diatomic molecules from the approximate solutions of the Schrodinger equation with Eckart plus inversely quadratic Yukawa potential

Journal of Molecular Modeling

We have obtained analytically the bound state solutions for the non-relativistic Schrodinger equation for the Eckart plus inversely quadratic Yukawa potential (EIQYP) using the parametric Nikiforov-Uvarov (NU) method. In order to validate our approximation, the bound state energies were computed and predicted for some selected diatomic molecules at different adjustable screening parameters from the available spectroscopic model parameters. The fact-finding obtained are in agreement with previously reported results available in literature. Furthermore, the graphs of the effective potential against inter-nuclear distance for low and high values of the screening parameters were reported. From our graphs, we observed that the approximation is best fit for very low values of the screening parameter α ≪ 1.

Solutions of the Schrödinger equation with Hulthén-screened Kratzer potential: Application to Diatomic Molecules

2

In this study, the Schrödinger equation with the Hulthén plus screened Kratzer potentials (HSKP) are solved via the Nikiforov-Uvarov (NU) and the series expansion methods. We obtained the energy equation and the wave function in closed form with Greene-Aldrich approximation via the NU method. The series expansion method was also used to obtain the energy equation of HSKP. Three distinct cases were obtained from the combined potentials. The energy eigenvalues of HSKP for HCl, LiH, H2, and NO diatomic molecules were computed for various quantum states. To test the accuracy of our results, we computed the bound states energy of HCl and LiH, for a special case of Kratzer and screened Kratzer potentials, which are in excellent agreement with the report of other researchers.

Expectation Values of Some Diatomic Molecules With Quantum Interaction Potential In Schrodinger Equation with Hellmann-Feynman Theorem Via Conventional Nikiforov-Uvarov Method

arXiv: Quantum Physics, 2017

In this work, we used a tool of conventional Nikiforov-Uvarov method to determine bound state solution of Schrodinger equation with quantum interaction potential called Hulthen-Yukawa inversely quadratic potential (HYIQP). We obtained the energy eigen values and the total wave function . We employed Hellmann-Feynmann Theorem (HFT) to compute expectation values for four different diatomic molecules: Hydrogen molecule (H2), Lithium hydride molecule (LiH), Hydrogen Chloride molecule (HCl) and Carbon(II)Oxide molecule. The resulting energy equation reduces to three well known potentials which are: Hulthen potential, Yukawa potential and inversely quadratic potential. We obtained the numerical bound state energies of the expectation values by implementing Matlab algorithm using experimentally determined spectroscopic constant for the different diatomic molecules. We developed a mathematica programming to obtain wave function and probability density plots for different orbital angular qua...

Exact solutions of the Schrödinger equation for the pseudoharmonic potential: an application to some diatomic molecules

Journal of Mathematical Chemistry, 2012

For arbitrary values n and quantum numbers, we present the solutions of the 3-dimensional Schrödinger wave equation with the pseudoharmonic potential via the SU (1, 1) Spectrum Generating Algebra (SGA) approach. The explicit bound state energies and eigenfunctions are obtained. The matrix elements r 2 and r d dr are obtained (in a closed form) directly from the creation and annihilation operators. In addition, by applying the Hellmann-Feynman theorem, the expectation values of r 2 and p 2 are obtained. The energy states, the expectation values of r 2 and p 2 and the Heisenberg uncertainty products (HUP) for set of diatomic molecules (CO, NO, O 2 , N 2 , CH, H 2 , ScH) for arbitrary values of n and quantum numbers are obtained. The results obtained are in excellent agreement with the available results in the literature. It is also shown that the HUP is obeyed for all diatomic molecules considered.