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arXiv:2303.00483 · Journal of Mathematical Physics

Quantum mechanics on sharply bent wires via two-interval Sturm-Liouville theory

João Paulo M. Pitelli, Ricardo Antonio Mosna, Felipe Felix Souto

Published Jun 1, 2024• 3 citations
arXivHTMLPDF

Abstract

We study quantum mechanics on the limiting case of a highly curved wire by approximating the physics around the curved region by three boundary condition parameters coming from the two-interval Sturm-Liouville theory. Since the geometric potential in this case is strong and non-integrable, these parameters depend crucially on the regularization of the curve. Hence, unless we know precisely the shape of the curve, any physical prediction is meaningless. In this context, the method presented in this paper becomes not only a useful approximation, but also a necessary scheme to deal with quantum mechanics on highly curved wires and (possibly) corners.

DOI
10.1063/5.0170587

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We study quantum mechanics on the limiting case of a highly curved wire by approximating the physics around the curved region by three boundary condition parameters coming from the two-interval Sturm-Liouville theory. Since the geometric potential in this case is strong and non-integrable, these parameters depend crucially on the regularization of the curve. Hence, unless we know precisely the shape of the curve, any physical prediction is meaningless. In this context, the method presented in this paper becomes not only a useful approximation, but also a necessary scheme to deal with quantum mechanics on highly curved wires and (possibly) corners.
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