Uncertainty Relation for Pseudo-Hermitian Quantum Systems
Quantum Physics
2025-08-11 v1
Abstract
This study investigates pseudo-Hermitian quantum mechanics, where the Hamiltonian satisfies a modified Hermiticity condition. We extend the uncertainty relation for such systems, demonstrating its equivalence to the standard Hermitian case within a pseudo-Hermitian inner product. Analytical solutions to the time-dependent Schr\"odinger equation with a linearly evolving potential are derived. Furthermore, we show that the uncertainty relation for position and momentum remains real and greater than 1/2, highlighting the significance of non-Hermitian systems in quantum mechanics.
Cite
@article{arxiv.2508.00648,
title = {Uncertainty Relation for Pseudo-Hermitian Quantum Systems},
author = {Boubakeur Khantoul and Bilel Hamil and Amar Benchikha},
journal= {arXiv preprint arXiv:2508.00648},
year = {2025}
}
Comments
10 pages, 1 figure