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.
Highlights
The more general exponential screened coulomb (MGESC) potential expressed as ( ) V (r ) =− V0 1+ (1+ αr ) e−2αr (1)r is a potential of great interest which on expansion comprises of the sum of coulomb potential, modified screened coulomb or the Yukawa potential and a modified exponential potential given as ( ) V r =− V0 r − V0 r e −2α r − V0α e−2αr (2)This potential is known to describe adequately the effective potential of a many-body system of a variety of fields such as the atomic, solid state, plasma and quantum field theory [1]
The bound state energy eigenvalues and the corresponding un-normalized eigenfunctions expressed in terms of hypergeometric functions were obtained
Potential variation with intermolecular distance (r) for some of the particles moving under the influence of MGESC, Yukawa and the mixed potential (MGESCY) were studied
Summary
The more general exponential screened coulomb (MGESC) potential expressed as ( ) V (r ) =− V0 1+ (1+ αr ) e−2αr (1). Screened Coulomb (GESC) potential with special emphasis on higher states and stronger interactions In his speculative studies, he obtained bound state solutions for both screened potentials via the Generalized Pseudospectral (GPS) method and computed reasonable results for the energy eigenvalues at different states compared with other results obtained in the literatures. In 1984 [13], carried out studies on a screened coulomb potential by using a Rayleigh-Schrodinger Perturbation theory and obtained energy eigen values for large values of screening parameters Their calculations to the energy eigenvalue yielded reasonable result compared to other numerical and analytical methods. Pakdel et al [17] studied the Dirac equation with scalar and vector potential for the Yukawa potential and obtained both bound and scattering states In their calculations, the energy eigenvalues for different values of n and k were reported numerically as well as their corresponding eigenstates. The aim of this report is to obtain bound state solutions of the Schrödinger equation for the More General Exponential Screened Coulomb Potential plus Yukawa (MGESCY) potential
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