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The Husimi distribution function and superposition of q-harmonic oscillator stationary states

We study a superposition of four stationary states of the q-deformed quantum harmonic oscillator in phase space, through the Husimi quasi-distribution function. This function is analytically computed and it consists of 16 parts, which are explicitly given in terms of q-shifted factorials. Our results are consistent with the known observation that the smoothing of the Wigner quasi-probability distribution through a filter of a size larger than h-bar restricts the appearance of any sub-Planck structures when q -> 0.