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Superposition and interference states in q-deformed quantum oscillator

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Abstract

Wave functions and probability density functions of superposition states of a q-deformed harmonic oscillator are studied. It is found that the intensity of the q deformation parameter and the ratio of probability amplitudes in the superposition state determine the oscillation characteristic of the probability density function. In the Fourier spectrum of the probability density function, high-frequency components disappear as the system evolves to an undeformed state. It is shown that by superposing four-wave functions with the same deformation value \(q=0.001\), an entangled state having sub-Planck features can be obtained, whereas two deformed states with the same q value do not constitute an entangled state.

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This manuscript has no associated data or the data will not be deposited. [Authors’ comment: Data sets generated during the current study are available from the corresponding author on reasonable request.]

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Acknowledgements

The authors would like to thank Sir Michael V. Berry (Emeritus, Melville Wills Professor of Physics, University of Bristol) for fruitful discussions.

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Authors and Affiliations

  1. Institute of Graduate Studies in Science, İstanbul University, Vezneciler, İstanbul, 34134, Türkiye

    Helda Alomeare

  2. Department of Physics, Faculty of Science, İstanbul University, Vezneciler, İstanbul, 34134, Türkiye

    Ferhat Nutku & Ekrem Aydiner

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  1. Helda Alomeare
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All authors contributed equally to the paper.

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Correspondence to Ferhat Nutku.

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Alomeare, H., Nutku, F. & Aydiner, E. Superposition and interference states in q-deformed quantum oscillator. Eur. Phys. J. D 78, 53 (2024). https://doi.org/10.1140/epjd/s10053-024-00855-1

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