Lyapunov control of a particle in a finite quantum potential well

A Lyapunov-based approach for the trajectory generation of a Schrodinger equation is proposed. For the case of a quantum particle in a 3-dimensional finite potential well with an arbitrary shape the convergence is precisely analyzed. Similar assumptions to those formerly used for the finite dimensional configurations ensure the quasi-global approximate stabilization of the partial differential equation around an isolated eigenstate of the free system. Dispersive estimates or Strichartz type are widely used for the proof of the convergence result.