  Starting from a potential with a continuum of energy eigenstates, we show how
the methods of supersymmetric quantum mechanics can be used to generate
families of potentials with bound states in the continuum [BICs]. We also find
the corresponding wave functions. Our method preserves the spectrum of the
original potential except it adds these discrete BICs at selected energies.
Specifically, we compute and graph potentials which have bound states in the
continuum starting from a null potential representing a free particle and from
both the attractive and the repulsive Coulomb potentials.
