Wilhelm Weber’s electrodynamics is an action-at-a-distance theory which has the property that equal charges inside a critical radius become attractive. Weber’s electrodynamics inside the critical radius can be interpreted as a classical Hamiltonian system whose kinetic energy is, however, expressed with respect to a Lorentzian metric. In this article we study the Schrödinger equation associated with this Hamiltonian system, and relate it to Weyl’s theory of singular Sturm–Liouville problems.

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韦伯核作为经典和量子力学系统的数学描述

威廉·韦伯的电动力学是一种远距离作用理论，其具有临界半径内的等电荷变得有吸引力的特性。临界半径内的韦伯电动力学可以解释为经典的哈密顿系统，但其动能是相对于洛伦兹度量来表达的。在本文中，我们研究与该哈密顿系统相关的薛定谔方程，并将其与韦尔的奇异斯特姆-刘维尔问题理论联系起来。