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arXiv · 2604.27018

Ground-state energy of a particle in a space with minimal length and minimal momentum

Arsen Panas·Volodymyr Tkachuk
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Abstract

In this article, we derived a rigorous lower bound on the ground-state energy for a class of one-dimensional quantum systems in deformed space with minimal coordinate and momentum uncertainties, representing the absolute minimum energy that is physically attainable. We considered a harmonic oscillator in such a space and calculate its ground-state energy. We generalized the problem to an a sufficiently broad class of potentials, deriving an equation for the coordinate uncertainty corresponding to the minimal energy, which can be solved numerically. Using a linear approximation in the deformation parameters, we obtained a general expression for the ground-state energy. We determined the domain of existence of solutions for the anharmonic oscillator potential with respect to the deformation parameters.

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Arsen Panas, Volodymyr Tkachuk. 2026-04-29. Ground-state energy of a particle in a space with minimal length and minimal momentum. https://arxiv.org/abs/2604.27018

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