Universal PSTD theory for solving quantum scattering in the Fresnel region and far-field

Scattering wave functions calculated using the novel pseudospectral-time-domain (PSTD) theory, and scattering amplitude calculated using the partial wave method. Numerical tests are conducted on several quantum potentials. Spherical potential barriers and wells of various heights/depths are set, andThe calculated far-field data: PSTD predictions vs. the strict results from the partial wave methods;Data of the Fresnel region vs. the far-field, calculated by PSTD;Evaluation of capability of the near-to-distant-field transformation by recovering the exact spherical wave function from the virtual surface data generate from the same spherical wave, to demonstrate the accuracy of the quantum surface equivalence theorem.