Quantum dynamics of hydrogen-like atom in one-dimensional box with oscillating walls

The quantum dynamics of a hydrogen-like atom confined in one-dimensional box with oscillating walls is studied. The description of the system is reduced to a one-dimensional Schrödinger equation for Coulomb potential with time-dependent boundary conditions, which is solved numerically. Using the obtained solution, the average kinetic energy and binding energies are calculated as a function of time. It is found that both the average kinetic energy and the binding energies are periodic in time with the period depending on the wall's oscillation parameters. The probability density is also analyzed as a function of time and coordinate.