Uncertainty Relation for Pseudo-Hermitian Quantum Systems

• URL: http://arxiv.org/abs/2508.00648v1
• Date: Fri, 01 Aug 2025 14:06:05 GMT
• Title: Uncertainty Relation for Pseudo-Hermitian Quantum Systems
• Authors: Boubakeur Khantoul, Bilel Hamil, Amar Benchikha,
• Abstract summary: We extend the uncertainty relation for such systems, demonstrating its equivalence to the standard Hermitian case within a pseudo-Hermitian inner product.<n>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.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• 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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