Is an electron a charge cloud? A reexamination of Schrödinger’s charge density hypothesis

This article re-examines Schrödinger’s charge density hypothesis, according to which the charge of an electron is distributed in the whole space, and the charge density in each position is proportional to the modulus squared of the wave function of the electron there. It is demonstrated that the charge distribution of a quantum system can be measured by protective measurements as expectation values of certain observables, and the results as predicted by quantum mechanics confirm Schrödinger’s original hypothesis. Moreover, the physical origin of the charge distribution is also investigated. It is argued that the charge distribution of a quantum system is effective, that is, it is formed by the ergodic motion of a localized particle with the charge of the system.