Non-Relativistics Treatment of Schrodinger Particle under Modified Inversly Quadratic Hellmann Potential Model Via Parametric N-U Method

Abstract

The non-relativistics study of particles under the modified inversely quadratic Hellmann potential has been studied. The energy eigenvalues and the corresponding wavefunction expressed in terms of the Jacobi polynomial are obtained using the parametric NU method. In obtaining the solutions for this system, we have used an approximation scheme to evaluate the centrifugal term (potential barrier). To test the accuracy of our result, we compared the approximation scheme with the centrifugal term and the result shows that there is an agreement between the centrifugal term and the approximation scheme for a very small screening parameter; showing that our potential is a short range potential. The results obtain from this work, would have many application in inner shield ionization problem, Electron core, Solid state Physics, Alkali-Hydride molecules. Three special cases of this potential have also been discussed.