An efficient approximation for accelerating convergence of the numerical power series. Results for the 1D Schrödinger's equation

2021/11/22 by A. Bagci, Bagci, A., Z. Guneş +1
Computer Science · Physics and Astronomy · #FOS: Physical sciences #Matrix Theory and Algorithms #Quantum Mechanics and Non-Hermitian Physics #Quantum Physics (quant-ph) #Scientific Research and Discoveries

paper · pdf · doi:10.48550/arxiv.2111.11379

openalex publication_date 2021/11/22 · openalex created_date 2022/10/17 · openalex updated_date 2026/07/28

Abstract

The numerical matrix Numerov algorithm is used to solve the stationary Schrödinger equation for central Coulomb potentials. An efficient approximation for accelerating the convergence is proposed. The Numerov method is error-prone if the magnitude of grid-size is not chosen properly. A number of rules so far, have been devised. The effectiveness of these rules decrease for more complicated equations. Efficiency of the technique used for accelerating the convergence is tested by allowing the grid-sizes to have variationally optimum values. The method presented in this study eliminates the increased margin of error while calculating the excited states. The results obtained for energy eigenvalues are compared with the literature. It is observed that, once the values of grid-sizes for hydrogen energy eigenvalues are obtained, they can simply be determined for the hydrogen iso-electronic series as, h_ε(Z)=h_ε(1)/Z.

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