Superposition and interference states in q-deformed quantum oscillator

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.