Bloch's theorem

Bloch's theorem states that electrons moving through a crystal, like a solid material, experience a repeating pattern of atomic structures. Despite this, their wave-like behavior can be described as a combination of a wave that repeats periodically and a smoothly varying function. Essentially, this means electrons can be thought of as having special states called "Bloch states" that extend across the entire crystal, allowing us to understand their movement and properties using mathematical models. This theorem is fundamental to understanding how materials conduct electricity and form the basis for semiconductor technology.