Solusi Semi Analitik Persamaan Schrödinger dari Osilator Harmonik dan Anharmonik yang Dipengaruhi Potensial Delta

Abstract

In this research a simple modeling will be made for BCS to the BEC crossover so it can be observed in dimension of space. Explanation of BCS to the BEC crossover will be modeled on the harmonic oscillator or anharmonik oscillator which influenced by delta potential and pairing constant (g) so the particles can be studied in dimensions of space . The purpose of this study is to observed the changes in the eigenfunctions and eigenvalues of the harmonic oscillator and the anharmonik oscillator due the influence of delta potensial on several g values . The results obtained in the ground state are the increase in the g values will make the eigenfunction localized at the point of equilibrium and it’s eigenvalues will drop. In other energy levels , increase in the g values will drop the eigenfunctions and eigenvalues to a saturation point with exception at odd level of the harmonic oscillator eigenfunction. Futhermore, in anharmonic oscillator, usage of g over a certain values can bring new eigenvalues and eigenfunctions.