Time-dependent wave packet’s dynamics of a particle confined in the linear potential

Abstract

This research investigates the time-dependent wave packet’s dynamics for a particle in a 1-D infinite deep quantum well disturbed by a linear potential. The interplay between quantum confinement and the linear potential significantly influences the wave packet’s dynamics of this system. Unlike the case of a particle in a 1-D quantum well, where the wave packet exhibits regular evolution and revival with an analytically determinable revival period, the introduction of the linear potential leads to discrete eigenenergy without an analytical expression, which makes accurate calculation of the revival period challenging. Results reveal that, for a given strength of the linear potential, regular evolution and revival of the wave packet occur only in a very small width of the quantum well; for larger widths of the quantum well, this behavior is lost. Additionally, for a given width of the quantum well, weak linear potential leads to regular periodic structures in the wave packet’s evolution, while stronger potential induces irregular oscillatory patterns. The revival period of this system can be evaluated through the autocorrelation function, which allows researchers to gain a deeper understanding of the dynamic behavior and periodic properties of wave packets. This study proposes a method to measure the revival period of a particle confined in the external potential, providing a pathway to a more precise understanding of intricate dynamics. Understanding these dynamics is crucial for applications in quantum computing, quantum confinement, and related technologies.

Graphical Abstract

The wave packet evolution of a particle in the confined linear potential. Suppose the strength of the electric field F = 0.001a.u. The width of the quantum well L = 10 a.u.