Quantum behaviour of particles

Question

What is the difference between classical particle and quantum particle?
I was thinking that we can distinguish between classical mechanics and quantum mechanics by changing our length scale. But I don't understood in what way or on what parameter we differentiate between classical particle and quantum particle.
you take one proton or neutron and say that it quantum particle, but when you make a solid out out of proton and neutron you say we have a classical body.
just a matter of size, I think?
just only size determines whether something will be a classical or quantum particle? or some inherent deep meaning?
There are no Question discussing Quantum and classical particle and can pose doubt to a beginner.

Vadim · Accepted Answer

The quantum and classical particles are governed by different principles and described by different equations. However, in a certain limit a quantum particle behaves like a classical one, which is expressed by the [Eherenfest theorem][1].
The relationship between quantum and classical is somewhat complex, as discussed, for example, in [this thread][2].
Update
In response to the updated question, let me first clarify the terminology.

Particle may mean different things, depending on the context. It can mean a point like object, i.e. an object whose internal structure is not essential for the problem that we are solving. Thus cars and stars are often treated as particles in mechanics. Particle may also mean an elementary particle - a special class of physical entities, such as electrons, protons, neutrons, photons, etc.
When speaking of classical and quantum one also has to distinguish between the actual physical world and mathematical formalisms that we use to model it. All the physical objects in this world are quantum and relativistic, but in many cases simplified classical description is quite appropriate for practical purposes.
Finally, it is necessary to mention that classical has special role in the sense that it is the limit most familiar to us from our conventional everyday experience, this is where we have most "intuition".
[1]: https://en.wikipedia.org/wiki/Ehrenfest_theorem
[2]: Is quantum mechanics applicable to only small things?

Jeff Bass · Answer

You seem to have the idea that quantum mechanics is simply given a different name because it is talking about smaller scales, but the truth is that the entire world is quantum mechanical including the macroscopic world. Quantum mechanics is a qualitatively different update to classical mechanics. We just didn't notice that we needed a better description of the world until we looked at small scales, since this is where quantum effects are most noticable.

Answered by Jeff Bass on February 23, 2021

Quantum behaviour of particles

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