Non-inertial effects on a non-relativistic quantum harmonic oscillator in the presence of a screw dislocation

Abstract

We investigate non-inertial effects induced by a rotating frame on a non-relativistic quantum harmonic oscillator as well as of the topology associated to a screw dislocation, which corresponds to a distortion of a vertical line into a vertical spiral. To do this, we obtain the analytical solutions of the time-independent Schrödinger equation for this harmonic oscillator potential in this background.The expressions for the energy spectrum are obtained and the solutions for four quantum states, namely n = 0, 1, 2 and 3, are analysed. Our results show that the presence of the topological defect (screw dislocation) as well the fact that we are analysing the system from the point of view of a rotating frame, changes the solutions of Schrödinger equation and the corresponding spectrum. Now these quantities depend on the angular velocity of the rotating frame, Ω, and also on the parameter β, which codifies the presence of the screw dislocation. Particularly, with respect to the energy spectrum of the system the changing is such that when Ω increases, the energy can increase or decrease depending on the values we assign to the eigenvalues of the angular and linear momenta.Additionally, we observe that the values of the parameter β that characterizes the screw dislocation causes a shift in the energy spectrum.