In the context of the event depending on the situation, there are different ideas to think of the electron.

In certain conditions it is possible to imagine the electron as the charge of a “ball”. In other cases it is possible to think of it as an emitted wave. Sometimes, it’s suitable to think of it as an undefined cloud. Sometimes, none of these theories are applicable, and it’s only a single vector in the Hilbert space.

The many ways to think about electrons are founded on

- The momentum, of the electron, or de Broglie length of an electron
- Relativistic in contrast to. quantum mechanics that are nonrelativistic as a crucial aspect
- Then it is it is also the frame used by the viewer.

Wave:

If the velocity that the electron has is low, or , in the same way the de Broglie wavelength greater than the length range you’re interested in the electron could be described as being a wave. If you conducted an interference test to observe the electron react to itself, then it’s acting as an oscillation.

If you’re interested in an electron that is bound to a nucleus and want to know where you can locate the electron, you could consider it an isolated wave, which is also called a “fuzzy cloud” that has a specific size that surrounds the nucleus.

Charged ball:

However when the momentum that the electron has is sufficiently high or, in the same way, the de Broglie wavelength is short enough, then it’s appropriate to consider an electron like a billiard ball charged with charge. This is a good idea for things that are much larger that the length of an electron. If you’ve got an electron beam inside the cathode tube (remember these? ) These electrons behave just like charged billiard ball.

Spinor field/Fourier representation

This regime isn’t able to go up to arbitrarily high energy levels. If you’ve got a high-energy electron, the quantum effects in relativity begin to take on greater significance. The definition that an electron is in Quantum Field Theory is one of the Dirac Spinor Field. The majority of the time the field (element of the Hilbert space) could be written as a vacuum state, with annihilation and creation operators operating on it. This is similar to thinking of electrons as a field of space that is divided into plane wave forms. One of the tools for calculation, Feynman diagrams, make the idea of”balls “ball” attractive (but the math remains an Fourier spatial representation therefore it’s not directly transformed to balls).

Frame dependence/Hilbert space vector:

In the end, it’s important to point that the number of particles that you think are present in the field is contingent on the frame in which the observer is. In flat spacetime QFT with observers only inertial The number operator is something that everyone is able to agree on. When you move into the curved spacetime, or add accelerometers and accelerating observers, the number operator is dependent on the frame (are you accelerating or inertial?). This means that it less useful to use the “ball” concept useless. The fundamental component that makes up Hilbert space and space are the same therefore it is the Hilbert space vector is an effective concept.