Stability and control of a confined 1D quantum system with time-dependent delta potentials

摘要

The evolution problem for a quantum particle confined in a 1D box and interacting with one fixed point through a time-dependent point interaction is considered. Under suitable assumptions of regularity for the time profile of the Hamiltonian, we prove the existence of strict solutions to the corresponding Schr?dinger equation. The result is used to discuss the stability and steady-state local controllability of the wavefunction when the strength of the interaction is used as a control parameter.