Accurate numerical solutions of the time-dependent Schrödinger equation

Details Accurate numerical solutions of the time-dependent Schrödinger equation Accurate numerical solutions of the time-dependent Schrödinger equation

2007-01-12

arxiv.org/abs/physics/0701150v1

Phys. Rev. E 75, 036707 (2007)

Physics

Computational Physics

10 pages, 5 figures

Scientific paper

10.1103/PhysRevE.75.036707

We present a generalization of the often-used Crank-Nicolson (CN) method of obtaining numerical solutions of the time-dependent Schr\"odinger equation. The generalization yields numerical solutions accurate to order $(\Delta x)^{2r-1}$ in space and $(\Delta t)^{2M}$ in time for any positive integers $r$ and $M$, while CN employ $r=M=1$. We note dramatic improvement in the attainable precision (circa 10 or greater orders of magnitude) along with several orders of magnitude reduction of computational time. The improved method is shown to lead to feasible studies of coherent-state oscillations with additional short-range interactions, wavepacket scattering, and long-time studies of decaying systems.

Affiliated with

Also associated with

No associations

Rating

Accurate numerical solutions of the time-dependent Schrödinger equation does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Accurate numerical solutions of the time-dependent Schrödinger equation, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Accurate numerical solutions of the time-dependent Schrödinger equation will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-218607