Penerapan Metode Modifikasi Runge Kutta Berdasarkan Rata-rata Harmonik pada Persamaan Schrödinger 1 Dimensi

Abstract

In this study the 1-dimensional Schrӧdinger equation was solved using numerical method. The Schrӧdinger equation is solved for the infinite potential well and the quantum harmonic oscillator. The classical 4th order Runge-Kutta method and the modified Runge-Kutta method of harmonic mean are used. The research begins by formulating a second-order differential equation for each problem. This second-order differential equation is then split into two ordinary differential equations so that it can be solved using the Runge-Kutta method. The results obtained from numerical calculations are the wave functions and energy levels for each quantum number n. The results of the wave function of the numerical solution show a very good trend and are in accordance with the wave function of the exact solution. Eigen energy values for each case have been obtained for various values of n. The largest error value of 0.58 % is obtained for the numerical solution using the modified Runge-Kutta method of harmonic mean.