The Second Order Effect of the Quantum Weyl Algebra on a Free Particle

Details The Second Order Effect of the Quantum Weyl Algebra on a Free Particle The Second Order Effect of the Quantum Weyl Algebra on a Free Particle

2010-02-26

arxiv.org/abs/1002.4936v1

Mathematics

Quantum Algebra

Scientific paper

In this paper we revisit and extend the work done by Chaturvedu et al, as well as Dabrowski and Parashar. The basic premise is to take a deformed coordinate system and give is a concrete realization. This realization is given by a parameter of q = exp (it). Expanding in powers of 't' and applying a deformed quantum Hamiltonian to a Free Particle yields a magnetic field. To first order we recover a constant magnetic field. To second order we recover an anisotropic magnetic field with an additional term. A brief mention is made about the quantum symmetries present within the quantum Weyl algebra.

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