Pythagorean
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ZapperZ said:I think this is a common reason why there is a misconception regarding what QM does.
First of all, you need to be clear on what is meant by "duality". In classical mechanics, you have to use a completely different set of description for particles, and then for waves. There is no direct relationship between those two. That is why it is inconceivable that in classical mechanics, something can exhibit both properties.
In QM, the "Hamiltonian" and the "Schrödinger Eqn" are essentially the same thing. We do not switch gears when we describe ALL of the properties of quantum object, whether they are behaving like a particle or a wave. The Marcella paper that I've highlighted several times show in painful details the QM formalism to describe photon diffraction and interference with multiple slits without invoking any "wave mechanics". And as you've said, the deBroglie relations shows a clear connection between "wavelike" and "particlelike" properties that is absent in classical mechanics. This shows that just ONE formulation can describe ALL of the observed phenomena, not two separate one. If we had discovered QM first ahead of classical mechanics, we would have never thought wavelike and particle like behavior to be different things, because we can describe them using the same starting point.
Zz.
Ok, thank you for your response. I never really thought of the definition of 'duality' in physics, since physics terms tend to look and sound like laymen terms but have different meaning. I guess I'm not really confused on the physics (well, not anymore than other undergrads at my level who haven't studied QM)
I see though, how it is a byproduct of the development of physics and the assumptions made in classical physics. The phrase 'particle-wave duality' is leftover from a time when it was a conflicting subject, when classical skeptics found it hard to believe that matter could behave synonymously as a wave and a particle.
EDIT: I totally just remember seeing the hamiltonian used with the schroedinger equation:
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