  We use a simple system, the electron configuration in a Hydrogen-like atom,
to demonstrate the importance of using a complete basis set to provide a proper
quantum mechanical description. We first start with what might be considered a
successful strategy --- to diagonalize a truncated Hamiltonian matrix, written
in a basis consisting of Hydrogen ($Z=1$) basis states. This fails to provide
the correct answer, and we then demonstrate that the continuum basis states
provided the rest of the true wave function, for the bound ground states. This
work then shows, in a relatively simple system, the need to utilize a complete
basis set, consisting of both bound and continuum states.
