  By performing a slow adiabatic change between two traps of a quantum
particle, it is possible to transform an eigenstate of the original trap into
the corresponding eigenstate of the final trap. If no level crossings are
involved, the process can be made faster than adiabatic by setting first the
interpolated evolution of the wave function from its initial to its final form
and inferring from this evolution the trap deformation. We find a simple and
compact formula which gives the trap shape at any time for any interpolation
scheme. It is applicable even in complicated scenarios where there is no
adiabatic process for the desired state-transformation, e.g., if the state
changes its topological properties. We illustrate its use for the expansion of
a harmonic trap, for the transformation of a harmonic trap into a linear trap
and into an arbitrary number of traps of a periodic structure. Finally, we
study the creation of a node exemplified by the passage from the ground state
to the first excited state of a harmonic oscillator.
