  A new post-Markovian quantum master equation is derived, that includes bath
memory effects via a phenomenologically introduced memory kernel k(t). The
derivation uses as a formal tool a probabilistic single-shot bath-measurement
process performed during the coupled system-bath evolution. The resulting
analytically solvable master equation interpolates between the exact
Nakajima-Zwanzig equation and the Markovian Lindblad equation. A necessary and
sufficient condition for complete positivity in terms of properties of k(t) is
presented, in addition to a prescription for the experimental determination of
k(t). The formalism is illustrated with examples.
