Transition to sub-Planck structures through the superposition of q-oscillator stationary states
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 1, and those of a compass state with the appearance of chessboard-type interference patterns when q 0.
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