Horner, J.S. (1977) Chebyshev Polynomials in the Solution of Ordinary and Partial Differential Equations. Doctor of Philosophy Thesis, Department of Mathematics, University of Wollongong, Wollongong. http://ro.uow.edu.au/theses/1543

has been cited by the following article:

• 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.