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Nyengeri, H., Simbizi, R., Girukwishaka, A., Nizigiyimana, R. and Ndenzako, E. (2018) Frobenius Series Solutions of the Schrodinger Equation with Various Types of Symmetric Hyperbolic Potentials in One Dimension. Open Access Library Journal, 5, 1-14.
https://doi.org/10.4236/oalib.1104728

has been cited by the following article:

• TITLE: Analytical Approximation to the Bound State Energies and Wave Functions of the Schrödinger Equation with the Gaussian Potential Well in One Dimension

  AUTHORS: Hippolyte Nyengeri, Rénovat Nizigiyimana, Rubin Ndikumana

  KEYWORDS: Schrödinger Equation, Bound States, Gaussian Potential Well, Modified Pöschl-Teller Potential, Time-Independent Perturbation Theory

  JOURNAL NAME: Open Access Library Journal, Vol.11 No.11, November 26, 2024

  ABSTRACT: In this paper, an efficient approximate analytical technique for solving the one-dimensional Schrödinger equation (SE) with an attractive Gaussian potential is developed. This technique is based on approximating the Gaussian potential well (GPW) with the modified Pöschl-Teller potential (MPTP), and on the first- and second-order perturbation treatment of the resulting bound state energies and wave functions. In order to illustrate the excellent performance of our technique, we compare our results with those obtained from the exact Hamiltonian diagonalization on a finite-real basis of associated Legendre functions (ALF).