近日，荷兰特文特大学Jan Klaers团队揭示量子粒子的能量-速度关系对玻姆力学提出了挑战。2025年7月2日出版的《自然》杂志发表了这项成果。

经典力学将粒子的动能（由于其运动而保持的能量）描述为始终为正。相比之下，量子力学使用波函数描述粒子的运动，其中可以出现负局部动能区域。当波函数的振幅经历显著衰减时，就会发生这种现象，这通常与量子隧穿有关。 

课题组研究了两个耦合波导系统中粒子的量子力学运动，其中波导之间的粒子数转移充当时钟，从而可以确定粒子沿波导轴的速度。通过将该方案应用于反射势阶的指数衰减量子态，研究组确定了具有负局部动能的粒子的能量-速度关系。结果发现，粒子的能量越小，换句话说，局部动能越负，势阶内的测量速度就越高。该发现为正在进行的隧道时间辩论做出了贡献，可以被视为对量子力学中Bohmian轨迹的测试。对于后者，研究组发现测量的能量-速度关系与玻姆力学中的引导方程所假设的粒子动力学不一致。

附：英文原文

Title: Energy–speed relationship of quantum particles challenges Bohmian mechanics

Author: Sharoglazova, Violetta, Puplauskis, Marius, Mattschas, Charlie, Toebes, Chris, Klaers, Jan

Issue&Volume: 2025-07-02

Abstract: Classical mechanics characterizes the kinetic energy of a particle, the energy it holds due to its motion, as consistently positive. By contrast, quantum mechanics describes the motion of particles using wave functions, in which regions of negative local kinetic energy can emerge1. This phenomenon occurs when the amplitude of the wave function experiences notable decay, typically associated with quantum tunnelling. Here, we investigate the quantum mechanical motion of particles in a system of two coupled waveguides, in which the population transfer between the waveguides acts as a clock, allowing particle speeds along the waveguide axis to be determined. By applying this scheme to exponentially decaying quantum states at a reflective potential step, we determine an energy–speed relationship for particles with negative local kinetic energy. We find that the smaller the energy of the particles—in other words, the more negative the local kinetic energy—the higher the measured speed inside the potential step. Our findings contribute to the ongoing tunnelling time debate2,3,4,5,6 and can be viewed as a test of Bohmian trajectories in quantum mechanics7,8,9. Regarding the latter, we find that the measured energy–speed relationship does not align with the particle dynamics postulated by the guiding equation in Bohmian mechanics.

DOI: 10.1038/s41586-025-09099-4

Source: https://www.nature.com/articles/s41586-025-09099-4