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can we perform an experiment which can show wave and particle nature at the same time? I think the answer is no. If that is the case, is that not what heisenberg uncertainty principle saying then.? or heisenberg uncertainty principle has some other meaning. Looks like uncertainty principle is direct consequence of dual nature but a limitation that you cant observe both the nature in a single experiment

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  • $\begingroup$ Things don't really behave as "particles or waves", they propagate as things called "wave packets" and the localisation of these wavepackets is responsible for their wave-iness or particle-ness. The localisation is down to the experiment, as the apparatus will interact with / measure different things. $\endgroup$ – user95137 Apr 6 '17 at 23:23
  • $\begingroup$ Then how do we see an interference pattern which follows a wave equãation.? $\endgroup$ – user31058 Apr 6 '17 at 23:29
  • $\begingroup$ The slit's size acts as a sort of measurement on the [talking about say, an electron] and Heisenberg's uncertainty relation results in the probability distribution for momentum and thus a diffraction pattern. $\endgroup$ – user95137 Apr 7 '17 at 0:24
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    $\begingroup$ things don't behave like waves or particles, they behave in quantum-mechanical way. $\endgroup$ – aaaaa says reinstate Monica Apr 7 '17 at 2:28
  • $\begingroup$ @aaaaaa please elucidate "quantum-mechanical way" $\endgroup$ – Pritt Balagopal Apr 7 '17 at 7:06
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Here is the result of the double-slit experiment, performed with a very low-intensity source of electrons (source: https://en.wikipedia.org/wiki/File:Elektronenbeugung_Doppelspalt_gerendert.png):

results

This result clearly shows both the wave and particle nature of the electron. The particle nature is apparent because we see from the image that individual electrons have a well-defined position when they interact with the detector (that is because the detector measures the position, collapsing the wavefunction). The wave nature is apparent because there is a diffraction pattern in the density of electrons.

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The whole concept of wave-particle duality is a very outdated one. The reality is that everything is fundamentally wavelike. However, sometimes the waves can take the form of a 'wave packet' in a what's known as a coherent state. These coherent states behave as if they were a classical particle, but really it's just a complex interaction between a superposition of waves that looks like it's behaving classically.

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Doing a Young's Double Slit experiment and photoelectric effect with the same light beam is an excellent way to experience both particle and wave nature of light. You could also do the same with electron beam to find the wave nature for these as well.

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Heisenberg's uncertainty principle refers to simultaneous measurements of different physical properties (as has been pointed out here, experiments may very well show particle and wave behaviour of the same entity), and is a consequence of quantum logic: non-commuting observables are incompatible physical properties, meaning they cannot exist in conjunction, so they cannot be measured simultaneously.

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