Quantum Mechanics on Sharply Bent Wires via Two-Interval Sturm-Liouville Theory
arXiv:2303.00483 · doi:10.1063/5.0170587
Abstract
We study quantum mechanics on a curved wire by approximating the physics around the curved region by three parameters coming from the boundary conditions given by the two interval Sturm-Liouville theory. Since the geometric potential on a highly curved wire is strong an non-integrable, these parameters depend on the regularization of the curved wire. Hence, unless we know precisely the shape of the wire, the presented method becomes not only a useful approximation, but also a necessary scheme to deal with quantum mechanics on highly curved wires.
8 pages, 11 figures