Abstract
We have obtained approximate bound state solutions of Schrödinger wave equation with modified quadratic Yukawa plus q-deformed Eckart potential Using Parametric Nikiforov-Uvarov (NU) method. However, we obtained numerical energy eigenvalues and un-normalized wave function using confluent hypergeometric function (Jacobi polynomial). With some modifications, our potential reduces to a well-known potential such as Poschl-Teller and exponential inversely quadratic potential. Numerical bound state energies were carried out using a well-designed Matlab algorithm while the plots were obtained using origin software. The result obtained is in agreement with that of the existing literature.
Highlights
Researchers have put on their interest over the years with the aim of investigating the bound state solutions of relativistic and nonrelativistic wave equations for different potentials
Various methods have been applied to obtain the solutions of the nonrelativistic wave equations with a chosen potential model
[16] has employed the asymptotic iteration method to calculate any l-state solutions of the Schrödinger equation with the Eckart potential by proper approximation of the centrifugal term
Summary
Researchers have put on their interest over the years with the aim of investigating the bound state solutions of relativistic and nonrelativistic wave equations for different potentials. With approximate analytical solution of the Yukawa potential with arbitrary momenta using the Nikiforov-Uvarov method, they obtained approximate analytical solutions of the radial Schrödinger equation for the Yukawa potential, and the energy eigenvalues and the corresponding eigen functions are calculated in closed forms [21]. After the above mentioned studies on these different potentials and their lofty importance, we seek to investigate the bound state solutions of the Schrodinger equation with the modified quadratic Yukawa plus q-deformed Eckart potential of the form:. Using the parametric NU method, we derive the energy bound state solutions and their wave functions of the Schrodinger equation for the modified quadratic Yukawa plus q-deformed Eckart potential, analytically and numerically.
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