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arXiv · 2508.00648

Uncertainty Relation for Pseudo-Hermitian Quantum Systems

Boubakeur Khantoul·Bilel Hamil·Amar Benchikha
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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.

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Boubakeur Khantoul, Bilel Hamil, Amar Benchikha. 2025-08-01. Uncertainty Relation for Pseudo-Hermitian Quantum Systems. https://doi.org/10.1007/s12648-025-03733-7

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