Solusi Problem Gaussian Pairing Dalam Basis Osilator Harmonik Menggunakan Teori Perturbasi Dan Metode Numerik

Abstract

This study aims to determine the profile of the energy and the wave function of a harmonic oscillator system under the effect of a Gaussian potential. This function can be used to model such fermions. The solution of this problem can be described by more efficiently using a perturbation theory based on the harmonic oscillator. The first four levels of energy and the wave function has been described using the analytical method and Numerical Methods . These results are displayed in graphical form . Wave function is shown in graphic form relation between the wave function and atomic distance, whereas energy shown in the form of relation between energy and the pairing constant g. From the graph shows that the ground state and the first excitation energy of the system will decrease with increasing pairing constant g, whereas for the higher excitation energy of the system increases with increasing pairing constant g. This is because when the system is in the ground state and the first excitation, the system tends to be localized in one place, whereas at higher excitation , the system will often be not only in one place, but some places are indicated by the peaks of density of system . Energy system obtained from the analytical and numerical methods haven’t significant. This is mean that to analize a higher excitation state can use numerical methods such as Numerov Method and Shooting Method to be more efficient