标题： 超带宽波包的自由时间演化：关于兔子和乌龟的量子故事 显示英文标题

标题： Free temporal evolution of a superbandwidth wave packet: The quantum tale of the hare and the tortoise

摘要： 量子力学与经典光学之间的相互作用能否为波包动力学提供新的视角？ 在此基础上，我们表明，在量子粒子自由传播过程中，可以出现同时具有超振荡和次振荡特性的局域动量。 这种行为在数学上类似于超带宽激光脉冲在色散介质中的传播，其中电场的瞬时频率表现出类似的次振荡和超振荡特性。 这种类比源于经典光学中光的波描述与量子力学形式主义之间的等价性。 此外，我们还探讨了在有限区域内自由传播过程中波包局域化的现象。 这种局域化直接与受限波包区域内的局域动量分布相关。 为了补充我们的量子力学分析，我们还进行了一项经典分析，以进一步了解这一现象。 我们的研究结果表明，具有次振荡和超振荡特性的局域动量的出现以及波包局域化都发生在特定的时间尺度内，我们将这个时间尺度定义为干涉时间。 显示英文摘要

摘要： Can the interplay between quantum mechanics and classical optics offer new perspectives on wavepacket dynamics? Building on this connection, we show that local momenta with both super-oscillatory and suboscillatory characteristics can arise during the free propagation of a quantum particle. This behavior is mathematically analogous to the propagation of a superbandwidth laser pulse in a dispersive medium, where the instantaneous frequencies of the electric field exhibit similar sub- and super-oscillatory features. This analogy is rooted in the equivalence between the wave description of light in classical optics and the formalism of quantum mechanics. In addition, we explore the phenomenon of wavepacket localization during free propagation within a bounded region. This localization is directly linked to the distribution of local momenta within the confined wavepacket region. To complement our quantum mechanical analysis, we also perform a classical analysis to provide further insights into this phenomenon. Our findings reveal that both the emergence of local momenta with sub- and super-oscillatory features and the wavepacket localization occur within a distinct timescale, which we define as the interference time.