Control of a Quantum Particle in a Moving Potential Well

Abstract The control is the potential well absolute position. For two kinds of potential shape (periodic and box), we propose approximated solutions to the stead-state motion planing problem: steering in finite time the particle from an initial well position to a final well position, the initial and final particle energies being identical. This problem is a quantum analogue of the water tank problem, where a tank filled with liquid is moved from one position where the surface is horizontal to another position where the surface is also horizontal