Solusi Persamaan Schrodinger Tidak Bergantung Waktu Dengan Metode Finite Difference

I Gusti Agung Widagda; I Nengah Artawan; Wayan Gede Suharta; I Gde Antha Kasmawan

doi:10.20527/flux.v21i3.19289

Solusi Persamaan Schrodinger Tidak Bergantung Waktu Dengan Metode Finite Difference

I Gusti Agung Widagda, I Nengah Artawan, Wayan Gede Suharta, I Gde Antha Kasmawan

Abstract

The solution of time-independent Schrodinger equation (TISE) has been studied by several researchers. In this research, a TISE solution is found by using the finite difference method which is implemented in computer program code by using the Python language. TISE in the form of a second order differential equation is solved by using the finite difference method. In order to normalize the resulting wave function it is necessary to divide it by square root of the integral of the squared wave function. The integral method used is the Riemann method. In order to prove quantitatively that the TISE solution of the finite difference method is the same as or close to that of the analytical method, it is carried out by using linear regression and the z test. The research results show that the linear regression results from the two methods are nearly close. This is able to be seen from the values of gradient (m), intercept (c) and coefficient of determination (R²) which are close to ideal values, namely, 1, 0 and 1, respectively. In addition, from the z test it is concluded that the null hypothesis H₀ is accepted, which means the solution of finite difference method is equal to analytical solution by a confidence level of 95 percent.

Keywords

eda hingga, Schrodinger, Riemann, uji z, regresi linear

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DOI: http://dx.doi.org/10.20527/flux.v21i3.19289