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\(\mathcal N\)-fold supersymmetry in quantum systems with position-dependent mass. (English) Zbl 1092.81031

The author of this interesting paper gives the framework of \(\mathcal{N}\)-fold supersymmetry in one-body quantum mechanical systems with position-dependent mass (PDM for short). The equivalence to weak quasi-solvability holds in the PDM case. A general procedure to construct a \(\mathcal{N}\)-fold supersymmetric PDM system is developed. As a result it is obtained the general form of type A\(\mathcal{N}\)-fold supersymmetry in PDM quantum systems. It turns out that the framework of \(\mathcal{N}\)-fold supersymmetry is quite powerful also in searching quasi-solvable PDM Hamiltonians. A pair of almost isospectral PDM Hamiltonians in the framework of \(\mathcal{N}\)-fold supersymmetry is obtained as well.

MSC:

81Q60 Supersymmetry and quantum mechanics
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