## $$\mathcal N$$-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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