Position-momentum uncertainty relations based on moments of arbitrary order
Steeve Zozor, Mariela Portesi, Pablo Sanchez-Moreno, Jesus S., Dehesa
TL;DR
This paper generalizes the Heisenberg uncertainty principle using moments of arbitrary order and Renyi entropy, providing improved bounds for quantum systems like hydrogenic and oscillator models.
Contribution
It introduces a new uncertainty relation based on moments of arbitrary order and Renyi entropy, enhancing previous formulations for multidimensional quantum systems.
Findings
Improved lower bounds for uncertainty relations in quantum systems.
Effective analysis for hydrogenic and oscillator-like systems.
Enhanced understanding of quantum uncertainty measures.
Abstract
The position-momentum uncertainty-like inequality based on moments of arbitrary order for d-dimensional quantum systems, which is a generalization of the celebrated Heisenberg formulation of the uncertainty principle, is improved here by use of the Renyi-entropy-based uncertainty relation. The accuracy of the resulting lower bound is physico-computationally analyzed for the two main prototypes in d-dimensional physics: the hydrogenic and oscillator-like systems.
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