Abstract
Supersymmetric quantum mechanics is constructed in a new non-Hermitian representation. Firstly, the map between the partner operators H (±) is chosen antilinear. Secondly, both these components of a super-Hamiltonian $$ \mathcal{H} $$ are defined along certain topologically non-trivial complex curves r (±)(x) which spread over several Riemann sheets of the wave function. The non-uniqueness of our choice of the map $$ \mathcal{T} $$ between ‘tobogganic’ partner curves r (+)(x) and r (−)(x) is emphasized.
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