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Title: The classical and quantum mechanics of a particle on a knot

A free particle is constrained to move on a knot obtained by winding around a putative torus. The classical equations of motion for this system are solved in a closed form. The exact energy eigenspectrum, in the thin torus limit, is obtained by mapping the time-independent Schrödinger equation to the Mathieu equation. In the general case, the eigenvalue problem is described by the Hill equation. Finite-thickness corrections are incorporated perturbatively by truncating the Hill equation. Comparisons and contrasts between this problem and the well-studied problem of a particle on a circle (planar rigid rotor) are performed throughout.
Authors:
Publication Date:
OSTI Identifier:
22451193
Resource Type:
Journal Article
Resource Relation:
Journal Name: Annals of Physics; Journal Volume: 359; Other Information: Copyright (c) 2015 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved.; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; EIGENVALUES; EQUATIONS OF MOTION; HILL EQUATION; MATHIEU EQUATION; QUANTUM MECHANICS; SCHROEDINGER EQUATION