κ-deformed quantum mechanics: Information entropies for the Mathews–Lakshmanan oscillator

Abstract

We study the problem of a position-dependent effective mass quantum system by means of the $\kappa$-formalism, focusing on the information entropies for the Mathews–Lakshmanan oscillator. We obtain the Shannon entropy in both position and wave-vector representations, for the ground and first excited states. Furthermore, the classical and semi-classical information entropies are obtained analytically; a logarithmic relationship with energy, that is linked to the anharmonicity of the oscillator, is reported.