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Planarizable Supersymmetric Quantum Toboggans
Symmetry, integrability and geometry: methods and applications, Tome 7 (2011) Cet article a éte moissonné depuis la source Math-Net.Ru

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In supersymmetric quantum mechanics the emergence of a singularity may lead to the breakdown of isospectrality between partner potentials. One of the regularization recipes is based on a topologically nontrivial, multisheeted complex deformations of the line of coordinate $x$ giving the so called quantum toboggan models (QTM). The consistent theoretical background of this recipe is briefly reviewed. Then, certain supersymmetric QTM pairs are shown exceptional and reducible to doublets of non-singular ordinary differential equations a.k.a. Sturm–Schrödinger equations containing a weighted energy $E\to E W(x)$ and living in single complex plane.
Keywords: supersymmetry; Schrödinger equation; complexified coordinates; changes of variables; single-complex-plane images of Riemann surfaces. 
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Miloslav Znojil. Planarizable Supersymmetric Quantum Toboggans. Symmetry, integrability and geometry: methods and applications, Tome 7 (2011). http://geodesic.mathdoc.fr/item/SIGMA_2011_7_a17/

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