Volume 132, Number 1, October 2020
|Number of page(s)||7|
|Published online||18 December 2020|
Quantum mechanics of a particle on a torus knot: Curvature and torsion effects
1 School of Physical Sciences, National Institute of Science Education and Research - Odisha, India
2 Physics and Applied Mathematics Unit, Indian Statistical Institute - Kolkata, West Bengal, India
Received: 23 May 2020
Accepted: 31 August 2020
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.
PACS: 03.65.Vf – Phases: geometric; dynamic or topological / 03.65.Sq – Semiclassical theories and applications
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