Physics, mathematics, and technology

2020 Issue №3

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On the question of extended two-dimensional non-re­lativistic supersymmetry



An algorithm for realizing the algebra of two-dimensional supersymmet­ric quantum mechanics is described. The cases N = 2 and N = 3 are described in detail. The procedure for iterating Darboux transformations is considered separately. In contrast to the one-dimensional case, in which the problem is completely solved by Krum's formulas, iterations of two-dimensional Dar­boux transformations remain insufficiently understood.