  We describe -- in a didactical and detailed way -- the so-called Lee model
(which shares similarities with the Jaynes-Cummings and Friedrichs models) as a
tool to study unstable quantum states/particles. This Lee model is based on
Quantum Mechanics (QM) but possesses some of the features of Quantum Field
Theory (QFT). The decay process can be studied in great detail and typical QFT
quantities such as propagator, one-loop resummation, and Feynman rules can be
introduced. Deviations from the exponential decay law as well as the Quantum
Zeno effects can be studied within this framework. The survival probability
amplitude as a Fourier transform of the energy distribution, the normalization
of the latter, and the Breit-Wigner limit can be obtained in a rigorous
mathematical approach.
