oalib

Publish in OALib Journal

ISSN: 2333-9721

APC: Only $99

Submit

Search Results: 1 - 2 of 2 matches for " Audace Girukwishaka "
All listed articles are free for downloading (OA Articles)
Page 1 /2
Display every page Item
Frobenius Series Solutions of the Schrodinger Equation with Various Types of Symmetric Hyperbolic Potentials in One Dimension  [PDF]
Hippolyte Nyengeri, René Simbizi, Audace Girukwishaka, Rénovat Nizigiyimana, Eugène Ndenzako
Open Access Library Journal (OALib Journal) , 2018, DOI: 10.4236/oalib.1104728
Abstract:
The Schrodinger equation (SE) for a certain class of symmetric hyperbolic potentials is solved with the aid of the Frobenius method (FM). The bound state energies are given as zeros of a calculable function. The calculated bound state energies are successively substituted into the recurrence relations for the expanding coefficients of the Frobenius series representing even and odd solutions in order to obtain wave functions associated with even and odd bound states. As illustrative examples, we consider the hyperbolic Poschl-Teller potential (HPTP) which is an exactly solvable potential, the Manning potential (MP) and a model of the Gaussian potential well (GPW). In each example, the bound state energies obtained by means of the FM are presented and compared with the exact results or the literature ones. In the case of the HPTP, we also make a comparison between exact bound state wave functions and the eigenfunctions obtained by means of the present approach. We find that our results are in good agreement with those given by other methods considered in this work, and that our class of potentials can be a perfect candidate to model the GPW.
Application of the Frobenius Method to the Schrodinger Equation for a Spherically Symmetric Hyperbolic Potential  [PDF]
Hippolyte Nyengeri, Rénovat Nizigiyima, Eugène Ndenzako, Félix Bigirimana, Dieudonné Niyonkuru, Audace Girukwishaka
Open Access Library Journal (OALib Journal) , 2018, DOI: 10.4236/oalib.1104950
Abstract:
In this paper, an efficient technique for computing the bound state energies and wave functions of the Schrodinger Equation (SE) associated with a new class of spherically symmetric hyperbolic potentials is developed. This technique is based on a recent approximation scheme for the orbital centrifugal term and on the use of the Frobenius method (FM). The bound state eigenvalues are given as zeros of calculable functions. The corresponding eigenfunctions can be obtained by substituting the calculated energies into the recurrence relations for the expanding coefficients of the Frobenius series representing the solution. The excellent performance of this technique is illustrated through numerical results for some special cases like Poschl-Teller potential (PTP), Manning-Rosen potential (MRP) and Poschl-Teller polynomial potential (PTPP), with an application to the Gaussian potential well (GPW). Comparison with other methods is presented. Our results agree noticeably with the previously reported ones.
Page 1 /2
Display every page Item


Home
Copyright © 2008-2017 Open Access Library. All rights reserved.