  We describe families of potentials which act as approximate cloaks for matter
waves, i.e., for solutions of the time-independent Schr\"odinger equation at
energy $E$, with applications to the design of ion traps. These are derived
from perfect cloaks for the conductivity and Helmholtz equations, by a
procedure we refer to as isotropic transformation optics. If $W$ is a potential
which is surrounded by a sequence $\{V_n^E\}_{n=1}^\infty$ of approximate
cloaks, then for generic $E$, asymptotically in $n$ (i) $W$ is both
undetectable and unaltered by matter waves originating externally to the cloak;
and (ii) the combined potential $W+V_n^E$ does not perturb waves outside the
cloak. On the other hand, for $E$ near a discrete set of energies, cloaking
{\it per se} fails and the approximate cloaks support wave functions
concentrated, or {\it almost trapped}, inside the cloaked region and negligible
outside. Applications include ion traps, almost invisible to matter waves or
customizable to support almost trapped states of arbitrary multiplicity.
Possible uses include simulation of abstract quantum systems, magnetically
tunable quantum beam switches, and illusions of singular magnetic fields.
