Dynamic two-level system in the presence of a delta-function pulse: Exactly solvable dynamic system

Department of Electrical and Electronics Engineering, Ariel University - Ariel 40700, Israel

Received: 1 May 2025
Accepted: 16 January 2026

Abstract

The Landau-Zener formula represents the only case where a dynamic quantum system was solved exactly analytically. There is no model of a system, which is perturbed by a temporal pulse, and can be solved exactly. It is suggested to use a delta-function perturbation, a model which has an exact analytical solution, to model the effect of a finite period pulse perturbation. Not only can this model be solved exactly and mimic the effect of a very narrow pulse, but it also presents a quantization rule for suppressed transmission (i.e., no change in initial state), which resembles qualitatively a similar quantization rule that appears due to the presence of a finite period pulse. Nevertheless, despite its simplicity, the model exhibits non-trivial dynamics that challenge approximation schemes. Specifically, it shows that the suppressed transmission criterion substantially changes due to an arbitrarily small change in potential value.