In the context of building solvable models in quantum mechanics
the authors come with an interesting combination of two ideas
which enables them to offer a few new models of the so called
Fermi-Ulam oscillators (in single spatial dimension) characterized
by the time-dependent (right) boundary condition. Separately, both
these ideas are well known. The first one (carrying the nickname
of supersymmetric quantum mechanics, cf. ref. [12]) enables the
authors to start from the most elementary and readily solvable
time-independent square well potential (cf. eq. (20)) and to
construct the whole hierarchy of the less trivial but still
exactly solvable ``partner" potentials (cf. the triplet of their
samples given by eqs. (27) and (37) and (42)). The second idea
(restricting the reader's attention to the separable
time-dependent Schroedinger equations) is then shown to produce
the final time-dependent exactly solvable versions of the
above-mentioned ``partner" potentials (cf. their respective
samples given by eqs. (30) and (39) and (44)) as well as the
corresponding energies and wave functions.

MR2400873 Jana, T. K.; Roy, P. A class of exactly solvable
Schrödinger equation with moving boundary condition. Phys. Lett. A
372 (2008), no. 14, 2368--2373. 81U05 (81Q60)