TL;DR
This paper introduces a q-deformed algebra of observables in quantum mechanics, deriving equations of motion that ensure unitarity, and explores solutions for simple models within a twisted deRham complex framework.
Contribution
It presents a novel formalism for quantum mechanics using q-deformed algebras and twisted deRham complexes, ensuring unitarity in the dynamics.
Findings
Derived equations of motion for q-deformed quantum systems
Ensured unitarity in the time evolution of the models
Solved the equations for simple quantum models
Abstract
We propose a new wiew on the structure of quantum mechanics and postulate a q-deformed algebra of observables. We find equations of motion for this system, which guarantee a unitary time developement. We solve this equations for simple models. We write this formalism in terms of twisted deRham complex.
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Taxonomy
TopicsAlgebraic structures and combinatorial models · Noncommutative and Quantum Gravity Theories · Advanced Topics in Algebra