Incoherent Scattering and the Concept of Discrete Electrons

Experiment has shown that scattered x-rays contain both a coherent and an incoherent portion. Classical electron theory provides a formula for scattering closely similar to that based on wave mechanics, but includes both coherent and incoherent components only if the atom consists of discrete electrons. From a comparison of the classical and wave-mechanics theories of scattering it is concluded that the most accurate classical analog of Schrödinger's $\psi {\psi }^{*}$ is the probability of occurrence of discrete electrons, and that a particular electron is associated with each particular function ${\psi }_n{{\psi }_n}^{*}$.