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Open Quantum Systems Decoherence

Boundary conditions for the Schrödinger equation in the numerical simulation of quantum systems

arXiv
Authors: Marco Patriarca

Year

2026

Paper ID

795

Status

Preprint

Abstract Read

~2 min

Abstract Words

118

Citations

N/A

Abstract

We study the problem of the boundary conditions in the numerical simulation of closed and open quantum systems, described by a Schrödinger equation. On one hand, we show that a closed quantum system is defined by local boundary conditions. On the other hand, we argue that, because of the uncertainty principle, no local boundary condition can be defined for open quantum systems. For this reason plane waves or wave packet trains cannot be simulated on a finite numerical lattice with the usual procedures. We suggest a method that avoids these difficulties by using only a small numerical lattice and maintains the correspondence with the physical picture, in which the incident and scattered waves may be infinitely extended.

Why This Paper Matters

  • This paper contributes to the Open Quantum Systems & Decoherence research area in the Quantum Articles archive.
  • It adds a 2026 reference point for readers tracking recent quantum research.
  • We study the problem of the boundary conditions in the numerical simulation of closed and open quantum systems, described by a Schrödinger equation.

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References & Citation Signals

[1] DOI https://doi.org/arXiv:2602.14654 [2] arXiv https://arxiv.org/abs/2602.14654 [3] Publisher https://arxiv.org/abs/2602.14654

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