On the quantization and generalized uncertainty relation for some quantum deformed algebras

TL;DR

This paper investigates the quantization and generalized uncertainty relations in quantum deformed algebras, revealing that for several cases, the position-momentum commutation resembles that in Planck scale deformed quantum mechanics.

Contribution

It demonstrates that certain quantum deformed algebras share the same position-momentum commutation relation as Planck scale deformed quantum mechanics.

Findings

Commutation relations are similar to Planck scale deformed quantum mechanics.

Analysis of quantization in specific quantum deformed algebras.

Insights into the structure of generalized uncertainty relations.

Abstract

In this paper, the quantization and generalized uncertainty relation for some quantum deformed algebras are investigated. For several deformed algebras, the commutation relation between the position and the momentum operator is shown to be the same as the one in the Planck scale deformed quantum mechanics.