| Popis: |
There has been much research in how to accurately and efficiently solve the time-dependent Schrodinger equation (TDSE) for scattering solutions within a bounded domain. A fruitful approach has involved the use of discrete transparent boundary conditions (DTBC), which have led to the elimination of spurious reflections at the boundaries of the spatial domain. The approach has been shown to improve the wave-function obtained as a function of the space step and time step, which is accurate to second order in the time step and fifth order in the space step. In this work, we discuss the solution of one-dimensional TDSE in a bounded domain subject to DTBC with higher order of accuracy which is accurate to fourth order in the time step. Then, we apply the approach to various forms of potential energy and snapshots of the wave function at a variety of times are given. |
