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arXiv · 1003.3167

Transition to sub-Planck structures through the superposition of q-oscillator stationary states

E. I. Jafarov·J. Van der Jeugt
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Abstract

We investigate the superposition of four different quantum states based on the $q$-oscillator. These quantum states are expressed by means of Rogers-Szeg\"o polynomials. We show that such a superposition has the properties of the quantum harmonic oscillator when $q\to 1$, and those of a compass state with the appearance of chessboard-type interference patterns when $q \to 0$.

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E. I. Jafarov, J. Van der Jeugt. 2010-03-16. Transition to sub-Planck structures through the superposition of q-oscillator stationary states. https://doi.org/10.1016/j.physleta.2010.06.046

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