Bound-state formation in time-dependent potentials

We study the temporal formation of quantum-mechanical bound states within a one-dimensional attractive square-well potential by first solving the time-independent Schrodinger equation and then studying a time -dependent system with an external time-dependent potential. For this we introduce Gaussian potentials with different spatial and temporal extensions and generalize this description also for subsequent pulses and for random noisy potentials. Our main goal is to study the timescales in which the bound state is populated and depopulated. Particularly, we clarify a likely connection between the uncertainty relation for energy and time and the transition time between different energy eigenstates. We demonstrate that the formation of states is not delayed due to the uncertainty relation but follows the pulse shape of the perturbation. In addition we investigate the (non-)applicability of first-order perturbation theory on the considered quantum system.

Automated summary

This study focuses on the temporal formation of quantum-mechanical bound states within a one-dimensional attractive square-well potential. By solving the Schrodinger equation and studying an external time-dependent potential, it explores the effects of different Gaussian potentials, subsequent pulses, and random noisy potentials on the bound states. The main goal is to analyze the timescales for state occupation and depopulation, as well as the potential connection between the uncertainty relation for energy and time and the transition time between different energy eigenstates.