Quantum mechanics of a particle on a torus knot: Curvature and torsion effects

Article Type

Research Article

Publication Title

EPL

Abstract

In this paper, we study the subtle effect of constraints on the quantum dynamics of a point particle moving on a non-trivial torus knot. The particle is kept on the knot by the constraints, generated by curvature and torsion. In the Geometry-Induced Potential (GIP) approach, the Schrödinger equation for the system yields new results in particle energy eigenvalues and eigenfunctions, in contrast with existing results that ignored curvature and torsion effects. Our results depend on Γ, parameter that characterizes the global features of both the embedding torus and, more interestingly, the knottedness of the path.

DOI

10.1209/0295-5075/132/10004

Publication Date

10-1-2020

Comments

Open Access, Green

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