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Probing Uncertainty Relations in Non-Commutative Space

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Abstract

In this paper, we compute uncertainty relations for non-commutative space and obtain a better lower bound than the standard one obtained from Heisenberg’s uncertainty relation. We also derive the reverse uncertainty relation for product and sum of uncertainties of two incompatible variables for one linear and another non-linear model of the harmonic oscillator. The non-linear model in non-commutating space yields two different expressions for Schrödinger and Heisenberg uncertainty relation. This distinction does not arise in commutative space, and even in the linear model of non-commutative space.

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Acknowledgments

We would like to thank Prof. Subir Ghosh of Physics and Applied Mathematics Unit, Indian Statistical Institute, Kolkata, for his valuable inputs and suggestions.

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Authors and Affiliations

  1. Cryptology and Security Research Unit, R.C. Bose Center for Cryptology and Security, Indian Statistical Institute, Kolkata, 700108, India

    Pritam Chattopadhyay & Goutam Paul

  2. Energetic Cosmos Laboratory, Nazarbayev University, Nur-Sultan, 010000, Kazakhstan

    Ayan Mitra

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  1. Pritam Chattopadhyay
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  2. Ayan Mitra
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Correspondence to Goutam Paul.

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Part of this work was done when the second author was visiting R. C. Bose Centre for Cryptology and Security of Indian Statistical Insitute as a Post-Doctoral Researcher during 2017.

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Chattopadhyay, P., Mitra, A. & Paul, G. Probing Uncertainty Relations in Non-Commutative Space. Int J Theor Phys 58, 2619–2631 (2019). https://doi.org/10.1007/s10773-019-04150-3

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