Western Illinois University, Physics, Macomb, IL 61455
Numerical solution to the time-dependent Schrodinger equation can be obtained using the split-step pseudo-spectral methods. The methods have a certain numerical order based on the splitting of the time evolution operator. We investigate the error behavior of different orders (first, second and fourth) in the context of scattering of a quantum particle from simple potentials, such as potential step, thin barrier and the time evolution of the bound states of the quantum harmonic oscillator.
[Abstract (DOCX)]