TITLE:
Application of the Economization of Power Series to Solving the Schrödinger Equation for the Gaussian Potential via the Asymptotic Iteration Method
AUTHORS:
Hippolyte Nyengeri, Benoit Manariyo, Rénovat Nizigiyimana, Salomon Mugisha
KEYWORDS:
Chebyshev Polynomials, Economization, Gaussian Potential, Asymptotic Iteration Method
JOURNAL NAME:
Open Access Library Journal,
Vol.7 No.7,
July
23,
2020
ABSTRACT: This paper presents economized power series for the Gaussian function. The economization is accomplished by utilizing the “usual” and the “shifted” Chebyshev polynomials of the first kind. The resulting economized series are applied to the solution of the radial Schrödinger equation with the attractive Gaussian potential via the asymptotic iteration method (AIM). The obtained bound state energies are compared with those given by the same method when the Taylor expansion is used to approximate the Gaussian potential. We also compare them with those obtained from the exact Hamiltonian diagonalization on a finite basis of Coulomb Sturmian functions.