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arXiv · 2210.02559

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

L. C. N. Santos·F. M. da Silva·C. E. Mota·V. B. Bezerra
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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.

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L. C. N. Santos, F. M. da Silva, C. E. Mota, V. B. Bezerra. 2022-10-04. Non-inertial effects on a non-relativistic quantum harmonic oscillator in the presence of a screw dislocation. https://doi.org/10.1142/s0219887823500676

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