  Experts know that bound state energy eigenvalues of a potential well are
poles of its transmission amplitude, $t(E)$. The textbooks do well by solving
the bound states and scattering states separately, but the connection goes
unheeded. Here, we present interesting and instructive illustrations, where we
extract bound state eigenvalues from the known transmission coefficients
$(T(E)=|t(E)|^2)$ for six analytically solvable potential wells.
