Parallel numerical method for nonlocal-in-time Schr\"odinger equation
Numerical Analysis
2018-09-21 v2 Distributed, Parallel, and Cluster Computing
Quantum Physics
Abstract
We present a new parallel numerical method for solving the non-stationary Schr\"odinger equation with linear nonlocal condition and time-dependent potential which does not commute with the stationary part of the Hamiltonian. The given problem is discretized in-time using a polynomial-based collocation scheme. We establish the conditions on the existence of solution to the discretized problem, estimate the accuracy of the discretized solution and propose the method how this solution can be approximately found in an efficient parallel manner.
Cite
@article{arxiv.1809.01516,
title = {Parallel numerical method for nonlocal-in-time Schr\"odinger equation},
author = {Dmytro Sytnyk},
journal= {arXiv preprint arXiv:1809.01516},
year = {2018}
}
Comments
Extended version of the original publication, several mistakes and typos were fixed, 1 figure