Comparizon of dynamic diffusion with explicit difference scheme for Shredinger equation

TL;DR

This paper compares the dynamic diffusion method with explicit finite difference schemes for solving the Schrödinger equation, highlighting differences in handling decoherence and the necessity of direct simulation.

Contribution

It introduces a comparison between dynamic diffusion and explicit difference schemes for Schrödinger equation solutions, emphasizing the unique aspects of dynamic diffusion.

Findings

Dynamic diffusion diverges from exact solutions with increasing particles.

Explicit finite difference schemes are contrasted with dynamic diffusion.

Simulation is essential for dynamic diffusion due to its non-reducibility to differential equations.

Abstract

We represent the method of dynamic diffusion for the approximate solution of Shroedinger equation with decoherence. Decoherence shows as the divergency of exact solution from the dynamics of diffusion swarm, which arises when the total number of real particles grows. The method of dnamic diffusion cannot be reduced to the solution of differential equations, in contrast to Bohm's quantum hydrodynamics, hence the direct computer simulation is the mandatory step of its development. We compare the dynamic diffusion with the explicit finite differences scheme for Shredinger equation for some standard one dimension cases.