  Using mainly two techniques, a point transformation and a time dependent
supersymmetry, we construct in sequence several quantum infinite potential
wells with a moving barrier. We depart from the well known system of a
one-dimensional particle in a box. With a point transformation, an infinite
square-well potential with a moving barrier is generated. Using time dependent
supersymmetry, the latter leads to a trigonometric P\"oschl-Teller potential
with a moving barrier. Finally, a confluent time dependent supersymmetry
transformation is implemented to generate new infinite potential wells, all of
them with a moving barrier. For all systems, solutions of the corresponding
time dependent Schr\"odinger equation fulfilling boundary conditions are
presented in a closed form.
