  We present a derivation of the Lindblad equation - an important tool for the
treatment of non-unitary evolutions - that is accessible to undergraduate
students in physics or mathematics with a basic background on quantum
mechanics. We consider a specific case, corresponding to a very simple
situation, where a primary system interacts with a bath of harmonic oscillators
at zero temperature, with an interaction Hamiltonian that resembles the
Jaynes-Cummings format. We start with the Born-Markov equation and, tracing out
the bath degrees of freedom, we obtain an equation in the Lindblad form. The
specific situation is very instructive, for it makes it easy to realize that
the Lindblads represent the effect on the main system caused by the interaction
with the bath, and that the Markov approximation is a fundamental condition for
the emergence of the Lindbladian operator. The formal derivation of the
Lindblad equation for a more general case requires the use of quantum dynamical
semi-groups and broader considerations regarding the environment and
temperature than we have considered in the particular case treated here.
