We analyse and explore some peculiar features of the generalized Pöschl–Teller potential. This particular potential can be tuned in terms of the allowed number of excited states, the shape of the potential, and the strength of the confinement. As an application we investigate the Bose–Einstein condensation of noninteracting 39K atoms in this trapping potential. We numerically study the effect of different tuning schemes of this particular potential on the dynamics of noninteracting BEC.
