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Some Further Notes on the Energy-Position/Momentum-Time Uncertainty Expressions for a Non-Relativistic Particle

Pavle Ilija Premović

Published Jan 1, 2018• 0 citations
OpenAlex

Abstract

Abstract. A brief discussion related to the energy-position and the momentum-time uncertainty relations is presented.

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Abstract In this paper we have explicitly computed the position-position and position-momentum (Heisenberg) uncertainty relations for the model of relativistic particles with arbitrary spin, proposed by Jackiw and Nair (J ackiw R. and N air V. P. Phys. Rev. D , 43 (1991) 1933) as a model for anyon, in a purely quantum mechanical framework. This supports (via Schwarz inequality) the conjecture that anyons live in a 2-dimensional non-commutative space. We have computed the non-trivial uncertainty relation between anyon coordinates, , using the recently constructed anyon wave function (M ajhi J. et al. , Phys. Rev. Lett. , 123 (2019) 164801), in the framework of B ialynicki -B irula I. and B ialynicka -B irula Z., New J. Phys. , 21 (2019) 07306. We also compute the Heisenberg (position-momentum) uncertainty relation for anyons. Lastly we show that the identical formalism when applied to electrons, yield a trivial position uncertainty relation, consistent with their living in a 3-dimensional commutative space.