Comparison of Dynamic Diffusion with an Explicit Difference Scheme for the Schrödinger Equation

Vladimir Kukushkin, Y. I. Ozhigov
2013 Complex Systems  
We represent the method of dynamic diffusion for the approximate solution of Schrödinger's equation with decoherence and describe a swarm simulation as a proof of concept. Decoherence occurs as the divergence of the exact solution for the dynamics of the diffusion swarm, which arises when the total number of real particles grows. The method of dynamic diffusion cannot be reduced to the solution of differential equations, in contrast to Bohm's quantum hydrodynamics; hence, direct computer
more » ... ion is the mandatory next step. We compare the dynamic diffusion with the explicit finite differences scheme for the Schrödinger equation for some standard one-dimension cases. Complex Systems, 22 There are three phases: explosion, flight, and rearrangement. 444 V. Kukushkin and Y. I. Ozhigov Complex Systems, 22
doi:10.25088/complexsystems.22.4.423 fatcat:lt6ksikeb5cmrg5loqg7ggsete