Planarizable Supersymmetric Quantum Toboggans

Details Planarizable Supersymmetric Quantum Toboggans Planarizable Supersymmetric Quantum Toboggans

2011-02-25

arxiv.org/abs/1102.5162v1

SIGMA 7:018,2011

Physics

Quantum Physics

Scientific paper

10.3842/SIGMA.2011.018

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-Schr\"odinger equations containing a weighted energy $E\to EW(x)$ and living in single complex plane.

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