[tel]

As an amateur, I think I follow most of this, at least at some level, but I don't follow why you'd unify the basis elements and particles. Thinking of a quantum harmonic oscillator, the eigenstates have some kind of localization that feels particle-like, but the oscillating pattern of a coherent solution seems "more particle-like" and arises out of the interference between those eigenstates. In particle-speak, I might try on a sentence like "this classical particle is generated by the interaction between... other... particles" but I'm clearly at a loss there.

On basis of that, I'd be more likely to say "QM needs to describe everything as a wave, and sometimes certain kinds of localized 'wave-packets' move around coherently, and that's what we'd call 'particles'". That also seems to gel with less coherent states where it feels like there's not really a particle to be found.

So, I'm curious why you'd prefer to relate the eigenstates themselves as particles. Again in the oscillator case, the eigenstates themselves seem less coherent and seem to behave less classically than I'd hope.

My best guess is that the property those states have that is not as well replicated by the "particle as a coherent wave packet phenomenon" is that they have well-defined energy quanta. But that's just a bit of a stab in the dark here. It perhaps makes more sense from the perspective of "particles are the things that we're able to measure in detectors" POV, though.

[ziofill]

You are exactly right at the end when you say that particles are what makes a detector go click. Let me try to clarify further. The "particleness" is not about localization, but about energy quantization. In fact, a single photon can be very non-localized, because spatial position is a different Hilbert space and it can be entirely independent of the energy. So the packets you are referring to are particles only if in their energy Hilbert space they correspond to a well-defined photon numbers, and that's why the analogy with classical particles only goes so far. To add to the confusion, one can speak of packets localized in phase space (e.g. coherent states, like the light produced by a laser) and packets localized in physical space like a short pulse, and these refer to different Hilbert spaces.