Abstract
Non-relativistic quantum effects of the topology of the spacetime with the distortion of a vertical line into a vertical spiral on the harmonic oscillator are investigated. By searching for analytical solutions to the Schrödinger equation in this topological defect background, it is shown that the topology of the spacetime modifies the spectrum of energy of the harmonic oscillator. Besides, it is shown that there exists an Aharonov–Bohm-type effect for bound states.
Highlights
Another perspective of searching for Aharonov–Bohmtype effects due to backgrounds of topological defect spacetimes was given in the non-relativistic limit
Eq (15) corresponds to the permitted energies associated with the radial mode n = 1 for a non-relativistic quantum particle confined to the harmonic oscillator in the spacetime with the distortion of a vertical line into a vertical spiral (1)
There are two contributions to the permitted energies related to the radial mode n = 1 that arise from the topology of the spacetime
Summary
Another perspective of searching for Aharonov–Bohmtype effects due to backgrounds of topological defect spacetimes was given in the non-relativistic limit. By dealing with the non-relativistic limit of the Klein–Gordon equation and the Dirac equation in topological defect spacetimes, it has been shown the connection with the elastic theory in solids [31,32]. Quantum effects associated with a spiral dislocation have been studied with geometric quantum phases [29] and the harmonic oscillator [44]. We follow this line of study that searches for Aharonov–Bohm-type effects in the non-relativistic limit. We analyse non-relativistic quantum effects on the harmonic oscillator in the spacetime with the distortion of a vertical line into a vertical spiral. We analyse the topological effects on the harmonic oscillator by showing that an analogue of the Aharonov–Bohm effect for bound states exists; in Sect. We analyse the topological effects on the harmonic oscillator by showing that an analogue of the Aharonov–Bohm effect for bound states exists; in Sect. 3, we present our conclusions
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