  Factorization of quantum mechanical potentials has a long history extending
back to the earliest days of the subject. In the present paper, the
non-uniqueness of the factorization is exploited to derive new isospectral
non-singular potentials. Many one-parameter families of potentials can be
generated from known potentials using a factorization that involves
superpotentials defined in terms of excited states of a potential. For these
cases an operator representation is available. If ladder operators are known
for the original potential, then a straightforward procedure exists for
defining such operators for its isospectral partners. The generality of the
method is illustrated with a number of examples which may have many possible
applications in atomic and molecular physics.
