Analytical solution of $D$ dimensional Schr\"odinger equation for Eckart potential with a new improved approximation in centrifugal term

• URL: http://arxiv.org/abs/2205.09024v1
• Date: Wed, 18 May 2022 16:01:51 GMT
• Title: Analytical solution of $D$ dimensional Schr\"odinger equation for Eckart potential with a new improved approximation in centrifugal term
• Authors: Debraj Nath and Amlan K. Roy
• Abstract summary: Analytical solutions are presented for eigenvalues, eigenfunctions of colorred 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.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• 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 $\ell \neq 0$ 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.

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