Technical report: a study of Schrödinger equation - analytical and Numerov method / Nur Shairani Mohd Shohaimi

Schrödinger equation is one of the basic equations of quantum mechanics. In this project, the series solution is used to solve the time independent Schrödinger equation for harmonic oscillator potential. The power-series expansion is used to calculate the energy of harmonic oscillators. The Numerov method is used to solve the Schrodinger in infinite spherical well. The results of harmonic oscillator and infinite spherical well are obtained by using MATLAB. The graphs of the wave function and probability distribution of a harmonic oscillator for n=O, l,2,3,4,5,10 are plotted. The wave function of hannonic oscillator potential has greater peaks near both edges and have a smallest amplitude and loop length near x = 0. The graphs of the radial part of wave function of infinite spherical well are plotted for angular quantum number (ℓ) =O, 1, 2, 3. The power series is suitable to calculate the wave function of harmonic oscillator potential and the Numerov method can be used to solve the radial equation for some values ℓ.