The dynamics of a particle in an expanding cavity is investigated in the Klein-Gordon framework in a regime in which the single-particle picture remains valid. The cavity expansion represents a time-dependent boundary condition for the relativistic wave function. We show that this expansion induces a non-local effect on the current density throughout the cavity. Our results indicate that a relativistic treatment still contains apparently spurious effects traditionally associated with the unbounded velocities inherent in non-relativistic solutions obtained from the Schrödinger equation. Possible reasons for this behaviour are discussed.

中文翻译：

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非局部性和时变边界条件：Klein-Gordon观点

在Klein-Gordon框架中，在单粒子图像保持有效的状态下研究了膨胀腔中粒子的动力学。腔扩展表示相对论波函数的时间相关边界条件。我们表明，这种膨胀引起整个腔体电流密度的非局部影响。我们的结果表明，相对论治疗仍然包含表面上虚假的效果，这些效果通常与从Schrödinger方程获得的非相对论解决方案固有的无限速度相关。讨论了此行为的可能原因。