Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)


SIGMA 7 (2011), 018, 24 pages      arXiv:1102.5162      http://dx.doi.org/10.3842/SIGMA.2011.018
Contribution to the Proceedings of the Workshop “Supersymmetric Quantum Mechanics and Spectral Design”

Planarizable Supersymmetric Quantum Toboggans

Miloslav Znojil
Nuclear Physics Institute ASCR, 250 68 Rez, Czech Republic

Received November 30, 2010, in final form February 21, 2011; Published online February 25, 2011

Abstract
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 EEW(x) and living in single complex plane.

Key words: supersymmetry; Schrödinger equation; complexified coordinates; changes of variables; single-complex-plane images of Riemann surfaces.

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