Some efficient schemes of variational iteration method for handling Schrödinger equations in quantum mechanics

Authors : Arzu Güleroğlu, Ece Güneş Zaralı

Pages : 94-109

Doi:10.25092/baunfbed.1470617

View : 86 | Download : 72

Publication Date : 2025-01-20

Article Type : Research Paper

Abstract :At the atomic level, one of the fundamental differential equations that describe the universe and everyday life is the Schrödinger equation in quantum mechanics. Solutions of Schrödinger equations have attracted the attention of researchers. In this study, the variational iteration method is used to handle three dimensional linear and nonlinear time dependent Schrödinger equations. Different iteration formulas have been constructed with the Lagrange multipliers. The accuracy of the approximate solutions obtained by using different iteration formulas of the variational iteration method is given with numerical examples. Comparisons of approximate solutions and exact solutions are shown with graphs. In addition, absolute error tables are included for these comparison results. As a result, it is seen that the variational iteration method gives approximations that converge to the exact solution more rapidly thanks to different iteration formulas.
Keywords : Analitik çözüm, varyasyonel iterasyon yöntemi, Schrödinger denklemi