  Supersymmetry allows one to build a hierarchy of Hamiltonians that share the
same spectral properties and which are pairwise connected through common
superpotentials. The iso-spectral properties of these Hamiltonians imply that
the dynamics and therefore control of different eigenstates are connected
through supersymmetric intertwining relations. In this work we explore how this
enables one to study general dynamics, shortcuts to adiabaticity (STA) and
quantum speed limits for distinct states of different supersymmetric partner
potentials by using the infinite box as an example.
