I have seen many questions on SE on the dual nature of electrons behaving in certain circumstances as particles and as waves in some other circumstance. There is one thing I couldn't get a clear answer on.
When making double slit experiment, we all agree that the electrons behave as waves. The same is true in atoms, where electron levels are described by Schrödinger equation. However, if we speak about a field like plasma physics (my field of work) and maybe beam physics, electrons are treated classically as particles with applying Newton's equation to describe their motion. The models built on particle treatment of electrons show an excellent agreement with experimental results.
From experimental results and testing, we know that electrons behave like waves (in double slit experiment) or as particles (gas discharge models). My question is, is experimenting the only way to decide which model (wave/particle) describes electrons better in particular circumstances? Isn't there any theoretical frame that decides whether electrons will behave as particles or wave in particular circumstance??
For the record, in plasma physics the strongest type of theoretical models is called Particle In Cell models (PIC). In those models Newton equation of motion is solved for a huge number of particles including electrons. Then the macroscopic properties are determined by averaging. This method although it treats electrons classically it is very successful in explaining what happens in experemints