Non-Relativistic Bound State Solutions of Modified Quadratic Yukawa plus q-Deformed Eckart Potential (original) (raw)
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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.
International Journal of Recent advances in Physics, 2014
In this work, we obtained an exact solution to Schrodinger equation using q-deformed Woods-Saxon plus modified Coulomb potential Using conventional Nikiforov-Uvarov method. We also obtained the energy eigen value and its associated total wave function. This potential with some suitable conditions reduces to two well known potentials namely: the Yukawa and coulomb potential. Finally, we obtained the numerical results for energy eigen value with different values of q as dimensionless parameter. The result shows that the values of the energies for different quantum number(n) is negative(bound state condition) and increases with an increase in the value of the dimensionless parameter(arbitrary constant). The graph in figure (1) shows the different energy levels for a particular quantum number.
European Journal of Applied Physics
Within the framework of Nikiforov-Uvarov method, we obtained an approximate solution of the Schrodinger equation for the Energy Dependent Generalized inverse quadratic Yukawa potential model. The bound state energy eigenvalues for were computed for various vibrational and rotational quantum numbers. Special cases were considered when the potential parameters were altered, resulting into Energy Dependent Kratzer and Kratzer potential, Energy Dependent Kratzer fues and Kratzer fues potential, Energy Dependent Inverse quadratic Yukawa and Inverse quadratic Yukawa Potential, Energy Dependent Yukawa (screened Coulomb) and Yukawa (screened Coulomb) potential, and Energy Dependent Coulomb and Coulomb potential, respectively. Their energy eigenvalues expressions and numerical computations agreed with the already existing literatures.
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.
Journal of Atomic and Molecular Physics, 2013
The solutions to the Schrödinger equation with inversely quadratic Yukawa and inversely quadratic Hellmann (IQYIQH) potential for any angular momentum quantum number have been presented using the Nikiforov-Uvarov method. The bound state energy eigenvalues and the corresponding unnormalized eigenfunctions are obtained in terms of the Laguerre polynomials. The NU method is related to the solutions in terms of generalized Jacobi polynomials. In the NU method, the Schrödinger equation is reduced to a generalized equation of hypergeometric type using the coordinate transformation = (). The equation then yields a form whose polynomial solutions are given by the well-known Rodrigues relation. With the introduction of the IQYIQH potential into the Schrödinger equation, the resultant equation is further transformed in such a way that certain polynomials with four different possible forms are obtained. Out of these forms, only one form is suitable for use in obtaining the energy eigenvalues and the corresponding eigenfunctions of the Schrödinger equation.
Journal of Nano- and Electronic Physics
The modified theories of noncommutative quantum mechanics have engrossed much attention in the last decade, especially its application to the fundamental three equations: Schrödinger, Klein-Gordon and Dirac equations. In this contextual exploration, we further investigate for modified quadratic Yukawa potential plus Mie-type potential (MIQYM) in the framework of modified nonrelativistic Schrödinger equation (MSE) using generalization of Bopp's shift method and standard perturbation theory instead of using directly the generalized Moyal-Weyl product method, we obtained modified energy eigenvalues and corresponding modified anisotropic Hamiltonian operator in both three dimensional noncommutative space and phase (NC-3D: RSP) symmetries.
Chinese Physics B, 2013
We study the D-dimensional Schrödinger equation for Eckart plus modified deformed Hylleraas potentials using the generalized parametric form of Nikiforov-Uvarov method. We obtain energy eigenvalues and the corresponding wave function expressed in terms of Jacobi polynomial. We also discussed two special cases of this potential comprises of the Hulthen potential and the Rosen-Morse potential in 3-Dimensions. Numerical results are also computed for the energy spectrum and the potentials, PACS Numbers: 03.65Ge, 03.65-w, 03.65Ca.
The solutions of the Schrӧdinger equation with Manning-Rosen plus a class of Yukawa potential (MRCYP) have been presented using the Pekeris-like approximation and parametric Nikiforov-Uvarov (NU) method. The bound state energy eigenvalues and the corresponding un-normalized eigen functions are obtained in terms of Jacobi polynomials. Also, inversely quadratic Yukawa, Yukawa, Manning-Rosen and coulomb potentials have been recovered from the mixed potential and their Eigen values obtained. The Numerical results are computed for some values of n at l = 0 with α = 0.01, 0.1, 2 and 5 using python 3.6 programming, and these results could be applied to molecules moving under the influence of MRYP potential as negative energy eigenvalues obtained indicate a bound state system.