Electrons, like other elementary particles, are often described as having a wave-particle duality. This means that they exhibit both wave-like and particle-like properties depending on how they are observed or measured.
When we say that electrons are "waves," it refers to their quantum nature described by the wave function in quantum mechanics. The wave function represents the probability distribution of finding an electron at different positions in space. It doesn't mean that the electron itself is a physical wave in the classical sense, but rather that its behavior and properties can be described using mathematical wave-like equations.
The wave function of an electron can take different shapes depending on its energy, momentum, and other properties. These shapes are determined by the solutions of the Schrödinger equation or other relevant quantum equations. The wave function may exhibit characteristics such as oscillations, nodes, and regions of constructive and destructive interference, as seen in phenomena like the double-slit experiment.
However, it's important to note that the wave function doesn't represent a physical "shape" of the electron in the way we typically think of solid objects having shapes. It describes the probability distribution of finding the electron at different positions if measured. The electron itself doesn't possess a well-defined position or shape until a measurement is made, at which point its wave function collapses to a specific position.
So, while the wave function can have different spatial profiles, it's important to understand that this is a mathematical representation of the electron's probabilistic behavior rather than a literal shape of the particle. The true nature of elementary particles, including electrons, is still a subject of ongoing research and exploration in the field of quantum mechanics.