Exact phase space localized projectors from energy eigenstates

In investigations of the emergence of classicality from quantum theory, a useful step is the construction of quantum operators corresponding to the classical notion that the system resides in a region of phase space. The simplest such constructions are approximate projection operators. Here, we show how to construct exact projection operators which are localized on regions of phase. We elucidate the properties of such operators and explore their time evolution. For the harmonic oscillator we find sets of phase space localized histories which are exactly decoherent for any initial state and have probability 1 for classical evolution.

► Exact projectors localized in phase space may be constructed.
► These projectors are a useful alternative to the quasi-projectors of Omnès.
► In simple models, an exact classical determinism in quantum mechanics exists.