Generalized Matrix Numerov Solutions to the Schr ̈odinger Equation

Abstract

 

 

The 1-D time-independent Schr ̈odinger equation is an ordinary differential equations that can be solved numerically using the well-known Numerov method. Recently the basic version of Numerov method has been recast into the Basic Matrix Numerov Method which has great advantage when used in modern high-level programming environments but produces results only to a limited accuracy. In this thesis, we recast the generalized

version of the Numerov method into the Generalized Matrix Numerov Method based on the algorithm of the existing Basic Matrix Numerov Method. The Generalized Matrix Numerov Method is capable of producing results to any desired accuracy. It is illustrated by finding stationary states with the corresponding energies and simulating the dynamics of Simple Harmonic Oscillator and Coupled Harmonic Oscillators, with the aid  mathematica . Results of varied accuracy are obtained, and highly accurate results are obtained with short CPU time, thus confirming the validity and effectiveness of this method.

 

https://www.physics.nus.edu.sg/wp-content/uploads/sites/5/2020/08/hyp-201314-32.pdf