Kevin Zelaya, Cinvestav, Mexico City

Title: Exactly solvable time-dependent potentials generated by Darboux and point transformations

The Darboux transformation is a useful tool used to construct new solvable stationary potentials in quantum mechanics. On the other hand, the point transformation is a geometrical transformation that allows us to deform a given differential equation. In this talk I show that, with the combined action of both the Darboux transformation and the class of form preserving point transformations, we can construct new solvable time-dependent potentials by departing from a stationary one. Moreover, the point transformation provide us a way to identify a spectral problem for the time-dependent system, with the latter, a complete set of orthonormal states at each time is found.