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

Abstract

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 for centrifugal term, from a combination of Greene-Aldrich and Pekeris approximations. Solutions are obtained in terms of hypergeometric functions. It facilitates an accurate representation in entire domain. Its validity is illustrated for energies in an arbitrary $\ell \ne 0$ quantum state. Results are compared for a chosen set of potential parameters in different dimensions. In short, a simple accurate approximation is offered for Eckart and other potentials in quantum mechanics, in higher dimension.

arXiv comment14 pages, 1 figure, 2 tables

References in corpus (13)

• Supersymmetry and Quantum Mechanics
• Solving the Schroedinger equation for bound states with Mathematica 3.0
• On the bound-state solutions of the Manning-Rosen potential including improved approximation to the orbital centrifugal term
• Bound state solutions of the Manning-Rosen potential
• The Hulthen Potential in D-dimensions
• Arbitrary $\ell$-state solutions of the Klein-Gordon equation with the Manning-Rosen plus a Class of Yukawa potentials
• Ro-vibrational energy and thermodynamic properties of molecules subjected to Deng-Fan potential through an improved approximation
• Analytical solutions of the Klein-Fock-Gordon equation with the Manning-Rosen potential plus a Ring-Shaped like potential
• Thermodynamic properties of diatomic molecules systems under anharmonic Eckart potential
• Studies on bound-state spectra of Manning-Rosen potential
• Analytical solutions of the Schrödinger equation with the Manning-Rosen potential plus a Ring-Shaped like potential
• Confinement in 3D polynomial oscillators through a generalized pseudospectral method
• Ro-vibrational energy analysis of Manning-Rosen and Pöschl-Teller potentials with a new improved approximation in the centrifugal term