One-dimensional quantum mechanical models obeying Smilga's weak supersymmetry are described in the matrix form. They are related to the parasupersymmetric and higher-order derivative deformations of the standard supersymmetric models discussed earlier. Their superconformal indices are computed and shown to be equivalent to the Witten indices for the second order supersymmetric quantum mechanics.
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V. P. Spiridonov (2024) studied this question.
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