  New families of time-dependent potentials related with the stationary
singular oscillator are introduced. This is achieved after noticing that a non
stationary quantum invariant can be constructed for the singular oscillator.
Such invariant depends on coefficients that are related to solutions of an
Ermakov equation, the latter becomes essential since it guarantees the
regularity of the solutions at each time. In this form, after applying the
factorization method to the quantum invariant, rather than the Hamiltonian, one
manages to introduce the time parameter into the transformation, leading to
factorized operators which are the constants of motion of the new
time-dependent potentials. Under the appropriate limit, the initial quantum
invariant reduces to the stationary singular oscillator Hamiltonian, in such
case, one recovers the families of potentials obtained through the conventional
factorization method and previously reported in the literature. In addition,
some special limits are discussed such that the singular barrier of the
potential vanishes, leading to non-singular time-dependent potentials.

Quantum Physics