Although the concept of the position-dependent effective masses
has been introduced, in the context of semiconductor theory, by
Oldwig von Roos as early as in 1983 (cf. the last cited paper
[52]), its popularity looks culminating at present, partially also
due to its appeal in the context of supersymmetric quantum
mechanics. The paper under review is in fact a continuation of
ref. [7] and it complements its results on a particle moving in a
semi-infinite layer based either on the separability or on the
shape-invariance techniques. The new approach turns attention to
the ideas connected with the superintegrability of the model (also
a growingly popular concept at present) and with the use of
deformed parafermionic operators (cf. ref. [36] for details
concerning the underlying algebra QR(3) etc). The new point of
view provides the third method of solution as well as some
entirely new results (e.g., on matrix elements of one of the
integrals of motion).

MR2322794 Quesne, Christiane Quadratic algebra approach to an
exactly solvable position-dependent mass Schrödinger equation in
two dimensions. SIGMA Symmetry Integrability Geom. Methods Appl. 3
(2007), Paper 067, 14 pp. (electronic). 81R12 (81R15)