Evolution of electron's particle view

In the early stages of solid state physics, electrons were treated as Newtonian particles obeying classical equations of motion. During the development of quantum mechanics in the first half of the 20th century, the wave nature of microscopic particles became the key to understanding various phenomena at the microscopic level. This deeply affected the perception of electrons in crystals:their eigenstates are Bloch waves while their particle nature only exists as the wave packet of Bloch waves on length scales greater than the atomic distance. After 1980, the geometric phase of Bloch waves began to play an indispensable role in modern condensed matter theory, completing the particle view of electrons in crystals. Here in this work we follow the general development of solid state physics, and demonstrate how the particle view of electrons in crystals evolved. Using several important topics as examples, we illustrate the key elements of the particle view and demonstrate its value in the study of solid state physics.