有限势阱中物质波散射的多级动力学

Miguel Ángel Mandujano, J. Villavicencio, R. Romo
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摘要

我们在量子快门模型的框架内,利用薛定谔方程的解析解,探索了有限势阱中物质波散射的动力学。我们发现,入射波会干扰量子井的束缚态,从而产生时域振荡。这些振荡表现出拉比型频率,其特征是入射波与量子阱束缚态之间的能量差。我们的研究表明,在具有双重束缚态的系统中,干涉模式的特征是随时间变化的概率密度中的量子节拍。这些跳动的周期取决于束缚态之间的能量差,而能量差可以通过控制势参数来调整。在系统频谱中束缚态、反束缚态和共振态共存的一般情况下,入射波与不同量子态的相互作用会引起概率密度的复杂振荡。我们证明,束缚态部门可以有效地描述这种复杂行为,为多级系统中的概率密度提供了一个简单可靠的分析表达式。该公式突出了束缚态的重要作用,束缚态与入射波的相互作用主导了瞬态概率密度。这与具有势垒和井的传统系统形成了鲜明对比,在传统系统中,共振控制着波的动力学。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Multilevel dynamics of matter waves scattering in finite potential wells
We explore the dynamics of matter wave scattering in finite potential wells using analytical solutions of the Schr"odinger equation within the framework of a quantum shutter model. We find that the incident wave interferes with the bound states of the quantum well, resulting in time-domain oscillations. These oscillations exhibit Rabi-type frequencies, characterised by the energy differences between the incident wave and the bound states of the quantum well. We show that in systems with double-bound states, the interference pattern is characterised by quantum beats in the time-dependent probability density. The period of these beatings depends on the energy difference between the bound states, which can be tuned by controlling the potential parameters. In the general case where bound, anti-bound, and resonant states coexist in the system spectrum, complex oscillations in the probability density arise from the interactions of the incident wave with different quantum states. We demonstrate that the bound states sector can effectively describe this complex behaviour, providing a simple and reliable analytical expression for the probability density in multilevel systems. This formula highlights the significant role of bound states, whose interaction with the incident wave dominates the transient probability density. This contrasts with conventional systems with potential barriers and wells, where resonances govern the wave dynamics.
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