Analytical solution of D dimensional Schrödinger equation for Eckart potential with a new improved approximation in centrifugal term

Analytical solutions are presented for eigenvalues, eigenfunctions of {\color{red} D-dimensional Schrodinger equation having Eckart potential} within Nikiforov-Uvarov method. This uses a new, improved approximation centrifugal term, from combination Greene-Aldrich and Pekeris approximations. Solutions obtained in terms hypergeometric functions. It facilitates an accurate representation entire domain. Its validity is illustrated energies arbitrary $\ell \neq 0$ quantum state. Results compared chosen set potential parameters different dimensions. In short, simple offered other potentials mechanics, higher dimension.