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I'm very confused about the applicability of classical vs quantum physics to describe a system. Suppose I have a system of particles and I want to describe their behavious, how do I know which theory applies to them? Is there a parameter that makes a system classical as opposed to quantum? Or should I try both theories and see which one agrees with experiment?

Qmechanic
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Ahmed Samir
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    Does this answer your question? When do you use Quantum Mechanics? – Thomas Fritsch Mar 19 '22 at 23:51
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    Maybe, I just don't know what the size of the structures refer to in this answer – Ahmed Samir Mar 20 '22 at 00:04
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    @AhmedSamir You could think of "size of structures" as the size of a particle. Logically speaking, quantum mechanics is always correct and classical mechanics is just an approximation that is useful in some situations. Practically speaking, it is much easier to solve classical equations than quantum ones, and classical mechanics is a very good approximation for a huge range of interesting phenomena. Loosely speaking, classical mechanics tends to be a good approximation if the system is big (has a lot of particles) and hot (so the system is not in its ground state). – Andrew Mar 20 '22 at 03:00
  • So, you don't need to do both and compare both to experiment. You just need to do both and compare them to each other. If they agree, classical mechanics is a good approximation. If they don't, quantum mechanics is right (or else, both are wrong, but so far no experiment goes against quantum mechanics). In practice it would be very expensive to actually do both a classical and a quantum calculation (except in trivial examples), so you really want to figure out in advance if classical mechanics is a good approximation. – Andrew Mar 20 '22 at 03:04

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Yes, I think that exist, the wavelength ($\lambda$) and the size of the system (L) are that parameters, L is the length of the size more representative.

Quantum mechanics is when $L \approx \lambda $.

Classical Mechanics is when $L >> \lambda $

I don't know what append $L << \lambda $, in electromagnetic theory the classification is electrical circuit ($\lambda >> L$), Microwave circuit ($\lambda \approx L$) and geometrical optics ($\lambda << L$).

Peralta_91
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  • what does system refer to here? – Ahmed Samir Mar 20 '22 at 00:00
  • Hello Peralta_91 and welcome to Physics SE. I am not sure your answer is correct. In general, there are systems used in various fields of physics that do not directly support quantum physics theories. For example Acoustics (which I am very familiar with) do not follow this "rule" you propose here. In most cases classical physics approaches are followed in order to describe those systems (with rare exceptions of some dissipation mechanisms related to atomic state transitions). Maybe you should edit your answer to be more specific. – ZaellixA Mar 20 '22 at 00:57