Abstract
In this work we study the similarity between the wave functions of q-deformed harmonic oscillator and wave functions of Cooper pair. The wave functions of Cooper pairs in coordinate-space have an “onion-like” layered structure with exponent decay (Boltzmann) envelope modulation. The ground state wave function of q-deform harmonic oscillator has the form of oscillate functions with Gaussian decay envelope modulation. The corresponding between Boltzmann and Gaussian forms of envelope functions and their quantum similarity are discussed.
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