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Every thing has a dual nature. So if we take waves(consider light interference) as particles, exactly what happens during interference (both constructive and destructive)? Can you explain in easy words since I have not studied physics at the university level.

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    $\begingroup$ Everything has a dual nature: I'm sorry, is that a universal principle? And to answer your question, we invoke the wavy nature of particles to explain interference, not the other way round. Waves in general (of sound, of light, of water) interfere, therefore when we observed that particles (such as the electron) produced the same interference patterns, we postulated the wave/particle duality. $\endgroup$
    – Demosthene
    Mar 25, 2015 at 17:45
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    $\begingroup$ It doesn't have to be only at the particle level. I have seen stadium "waves" (made of thousands of people) interact and cancel. $\endgroup$
    – Jiminion
    Mar 25, 2015 at 17:51

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You ask what happens if matter (de Broglie) waves interfere coherently, expressed in a particle picture. That is adding two quantum states coherently, either in-phase (constructive interference) or 180 degree out of phase (destructive interference).

If you have seen (light) interference patterns, you have basically already observed this effect: Your eyes or your camera detects photons. These occur where the photon matter wave (or, here equivalently, electromagnetic waves) interfere as described.

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You can't consider them as particles in this case.

The wave/particle is neither a classical wave, nor a classical particle, but a different entity, described by quantum mechanics. This quantum mechanical description, done, e.g., by a wave function or a field, implies Original Post's wave-particle duality.

And the point here is that this duality doesn't mean that you can always choose either wave or particle description, but that, depending on the physical setting, a wave-like or particle-like behavior is observed. So some behaviors, such as interference, can only be understood in the wave description - if you try to use a particle description here, you'll make predictions that contradict experimental observation.

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