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Supersymmetric quantum mechanics living on topologically non-trivial Riemann surfaces

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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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Authors and Affiliations

  1. Nuclear Physics Institute ASCR, 250 68, Řež, Czech Republic

    Miloslav Znojil

  2. Departamento de Física, Universidad de Santiago de Chile, Casilla 307, Santiago 2, Chile

    Vít Jakubský

Authors
  1. Miloslav Znojil
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  2. Vít Jakubský
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Correspondence to Miloslav Znojil.

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Znojil, M., Jakubský, V. Supersymmetric quantum mechanics living on topologically non-trivial Riemann surfaces. Pramana - J Phys 73, 397–404 (2009). https://doi.org/10.1007/s12043-009-0131-7

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  • DOI: https://doi.org/10.1007/s12043-009-0131-7

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