标题： 超光速物质波 显示英文标题

标题： Superluminal matter waves

摘要： 狄拉克方程自出现以来，一直是现代物理学最伟大的成功之一，它是第一个与狭义相对论完全兼容的量子力学理论。 这种兼容性确保了速度的期望值小于真空中的光速。 在这里，我们表明，狄拉克方程允许自由粒子解，其中波函数的峰值振幅可以以任何速度传播，包括超过真空光速的速度，尽管其速度期望值是亚光速的。 这些解是通过在动量空间中叠加具有相关性的基函数构建的。 这些任意速度的波函数具有近似恒定的轮廓，并可能影响对概率密度局部值敏感而非期望值的量子力学过程。 显示英文摘要

摘要： The Dirac equation has resided among the greatest successes of modern physics since its emergence as the first quantum mechanical theory fully compatible with special relativity. This compatibility ensures that the expectation value of the velocity is less than the vacuum speed of light. Here, we show that the Dirac equation admits free-particle solutions where the peak amplitude of the wavefunction can travel at any velocity, including those exceeding the vacuum speed of light, despite having a subluminal velocity expectation value. The solutions are constructed by superposing basis functions with correlations in momentum space. These arbitrary velocity wavefunctions feature a near-constant profile and may impact quantum mechanical processes that are sensitive to the local value of the probability density as opposed to expectation values.