When can a single particle be treated classically?
I feel like after 15 years of doing physics I ought to know the answer to this question, but I don't. Here are two variants that will help describe my confusion:
1) When can a single, free, non-relativistic particle be treated classically?
I assume the answer is "never", since wave packets spread so fast. So, while the expectation value of the position of the particle moves in a straight line like a classical particle, the probability of finding it on the classical trajectory is basically zero.
2) When can a single charged particle in an external electromagnetic field be treated classically?
I would have also guessed "never" by similar reasoning to point 1. However, textbooks are full of statements about electrons following the Lorentz force law. Wikipedia even has a picture of electrons in a "teltron tube". Every plasma physics textbook stats with N classical particles (electrons/ions) interacting by the Lorentz force. What is going on? What is the justification for this approximation? Is it secretly some statistical statement valid only for large N (i.e. the words are wrong but the kinetic equations are correct)? Is there any reference that discusses this? I cannot see how a single particle can ever be treated classically.
Note: I am not asking why macroscopic bodies behave classically. That's an interesting question but there is a lot of work on it. I am also not asking about special configurations like coherent states in a harmonic potential. I am asking about single (say, elementary) particles in generic situations.