  Green's functions in Physics have proven to be a valuable tool for
understanding fundamental concepts in different branches, such as
electrodynamics, solid-state and many -body problems. In quantum mechanics
advanced courses, Green's functions usually are explained in the context of the
scattering problem by a central force. However, their use for more basic
problems is not often implemented. The present work introduces Green's Function
in quantum mechanics courses with some examples that can be solved with
essential tools. For this, the general aspects of the theory are shown,
emphasizing the solution of different fundamental issues of quantum mechanics
from this approach. In particular, we introduce the time-independent Green's
functions and the Dyson equation to solve problems with an external potential.
As examples, we show the scattering by a Dirac delta barrier, where the
reflection and transmission coefficients are found. In addition, the infinite
square potential well energy levels, and the local density of states, are
calculated.
