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arXiv · 0904.2294

Supersymmetric quantum mechanics living on topologically nontrivial Riemann surfaces

Miloslav Znojil·Vit Jakubsky
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Abstract

Supersymmetric quantum mechanics is constructed in a new non-Hermitian representation. Firstly, the map between the partner operators $H^{(\pm)}$ is chosen antilinear. Secondly, both these components of a super-Hamiltonian ${\cal H}$ are defined along certain topologically nontrivial complex curves $r^{(\pm)}(x)$ which spread over several Riemann sheets of the wave function. The non-uniqueness of our choice of the map ${\cal T}$ between "tobogganic" partner curves $r^{(+)}(x)$ and $r^{(-)}(x)$ is emphasized.

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Miloslav Znojil, Vit Jakubsky. 2009-04-15. Supersymmetric quantum mechanics living on topologically nontrivial Riemann surfaces. https://doi.org/10.1007/s12043-009-0131-7

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