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Quantum mechanics contains and explains classical physics, but
the converse is not true. Really not. It makes no sense to try
to explain (much less define) QM directly in terms of classical
particles or waves.
Quantum mechanics is not classical, except in certain limits.
Classical waves are a classical idea.
Classical particles are a classical idea.
So, again: It makes no sense to try to explain (much less
define) QM directly in terms of classical particles or waves.
Rather than saying something is both a wave and a particle, I
prefer to say it is neither. That is: In QM there is only stuff.
Sometimes stuff looks sorta like a classical wave and sometimes
stuff looks sorta like a classical particle, but mostly it's
just stuff. Sui generis.
We can use analogies to hint at the nature of real (i.e.
quantum mechanical) universe, in the same way that it is
possible to communicate the idea of "blue triangle" without
actually exhibiting one:
https://av8n.com/physics/img48/blue-triangle.png
It takes a big leap of the imagination to go from things we can
get our arms around to the real quantum mechanical stuff.
The leap is much bigger than can be captured by the idea of
"duality".