  The necessity and utility of considering the interaction of a quantum system
with its environment when describing its time evolution have been recognized in
several branches of physics and of other sciences. The Kraus' representation is
a general and succinct approach to describe such open system dynamics in a wide
range of relevant physical scenarios. In this article, by abdicating from the
generality of the formalism of quantum operations and with this avoiding its
associated complications, we show in a simple manner how we can obtain the
Kraus' representation using basically the closed system (system plus
environment) unitary dynamics and the partial trace function. The example of a
two-level atom interacting with the vacuum of the electromagnetic field is
regarded for the sake of instantiating this formalism, which is then applied to
study the time evolution of the atom's quantum coherence.
