Numerical quantum evolution of confined particle with non-periodic boundary conditions through split operator method reconstructed by Gegenbauer series

Abstract

The computation of the quantum evolution of a spatially confined particle with non-periodic boundary conditions is considered. The operator split method is used to evolve the eigenfunctions. This involves two fourier reconstruction and manifests Gibbs phenomenon under non-periodic boundary condition. The split operator method is reconstructed through Gegenbauer series. It is shown that Gegenbauer reconstruction minimizes the manifestations of Gibbs phenomenon.