TITLE:
Bound State Solutions of the Schrödinger Equation for the More General Exponential Screened Coulomb Potential Plus Yukawa (MGESCY) Potential Using Nikiforov-Uvarov Method
AUTHORS:
B. I. Ita, H. Louis, O. U. Akakuru, T. O. Magu, I. Joseph, P. Tchoua, P. I. Amos, I. Effiong, N. A. Nzeata
KEYWORDS:
Yukawa, Exponential Screened Coulomb, Schrodinger, Hypergeometric
JOURNAL NAME:
Journal of Quantum Information Science,
Vol.8 No.1,
March
30,
2018
ABSTRACT: The solutions of the Schrödinger with more general exponential
screened coulomb (MGESC), Yukawa potential (YP) and the sum of the mixed potential
(MGESCY) have been presented using the Parametric Nikiforov-Uvarov Method (pNUM).
The bound state energy eigenvalues and the corresponding un-normalized eigenfunctions
expressed in terms of hypergeometric functions were obtained. Some derived equations
were used to calculate numerical values for MGESC, YP, and MGESCY potentials for
diatomic molecules with different screening parameters (α) for l = 0 and l = 1 state with V0 = 2.75 MeV and V1 = 2.075 MeV. We observed an increase in l value; the particles behave more repulsive
than attractive. The numerical values for different l-states at different screening
parameters for CO molecules (r = 1.21282)
and NO molecule (r = 1.1508) were obtained
using the bound state energy eigenvalue of the Schrodinger equation for MGESC, YP
and MGESCY potentials. Potential variation with intermolecular distance (r) for some of the particles moving under
the influence of MGESC, Yukawa and the mixed potential (MGESCY) were also studied.
We also observed the variation of the MGESC potential with the radial distance of
separation between the interacting particles (r) for different screening parameters (α) with V0 = 2.75
MeV at l = 0 and l = 1 and YP with V1 = 2.075 MeV at l = 0 and l = 1 as purely diatomic particles in nature.
The energies plotted against the principal quantum number n for different values
of (α) for both CO and NO show closed
resemblance even at different values of the potential depth. The energy plots of
the YP and MGESC potential for both CO and NO molecules as n→∞, and the energy E→0, shows
exothermal behaviour. The energy expression for the mixed potentials V0 = 5 MeV and V1 = 10 MeV, shows that both diatomic molecules possesses
similar behaviour.