Solutions for a q-generalized Schr\"odinger equation of entangled interacting particles

TL;DR

This paper explores solutions to a q-generalized Schrödinger equation for two entangled particles, revealing unique behaviors like ring-shaped wave functions and conditions for frozen states, extending understanding of quantum systems with non-standard dynamics.

Contribution

It provides analytical and numerical solutions for the q-generalized Schrödinger equation with two particles, including cases with time-dependent potentials and new phenomena at specific q-values.

Findings

Wave function exhibits ring-like shape at q=2.

Frozen states occur only for special parameters at q=3.

Standard Schrödinger equation recovered as q approaches 1.

Abstract

We report on the time dependent solutions of the $q-$generalized Schr\"odinger equation proposed by Nobre et al. [Phys. Rev. Lett. 106, 140601 (2011)]. Here we investigate the case of two free particles and also the case where two particles were subjected to a Moshinsky-like potential with time dependent coefficients. We work out analytical and numerical solutions for different values of the parameter $q$ and also show that the usual Schr\"odinger equation is recovered in the limit of $q\rightarrow 1$. An intriguing behavior was observed for $q=2$, where the wave function displays a ring-like shape, indicating a bind behavior of the particles. Differently from the results previously reported for the case of one particle, frozen states appear only for special combinations of the wave function parameters in case of $q=3$.