  Transformation optics constructions have allowed the design of
electromagnetic, acoustic and quantum parameters that steer waves around a
region without penetrating it, so that the region is hidden from external
observations. The material parameters are anisotropic, and singular at the
interface between the cloaked and uncloaked regions, making physical
realization a challenge.
  We address this problem by showing how to construct {\sl isotropic and
nonsingular} parameters that give {\sl approximate} cloaking to any desired
degree of accuracy for electrostatic, acoustic and quantum waves. The
techniques used here may be applicable to a wider range of transformation
optics designs.
  For the Helmholtz equation, cloaking is possible outside a discrete set of
frequencies or energies, namely the Neumann eigenvalues of the cloaked region.
For the frequencies or energies corresponding to the Neumann eigenvalues of the
cloaked region, the ideal cloak supports trapped states; near these energies,
an approximate cloak supports {\sl almost trapped states}. This is in fact a
useful feature, and we conclude by giving several quantum mechanical
applications.
