Do both electrons and protons have wave and particle properties and if they do, do they show them at the same time?

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    $\begingroup$ Remember, they are not real waves but rather probability amplitudes that is probability waves. They are both simultaneously associated with probability waves. Think of the atom where the electrons are described with standing waves. $\endgroup$ – user5764 Sep 10 '15 at 17:42
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    $\begingroup$ @user36790 Technically you are espousing the Copenhagen interpretation and there are many other interpretations of quantum mechnics. While the Copenhagen interpretation is the most popular method of interpreting the Schrödinger equation, there are many other explanations that do not interpret $\Psi$ as a probability amplitude and $\Psi^*\Psi$ as probability density. $\endgroup$ – Jonathon Sep 10 '15 at 18:49
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    $\begingroup$ @Jonathon: You are absolutely correct. By far, however, the best theory is Quantum Field Theory. Nevertheless, I thought it would be better to talk about the conventional one:) $\endgroup$ – user5764 Sep 10 '15 at 18:52
  • $\begingroup$ I would say that both wave and particle properties aren't "shown at the same time." Our perception of particle or wave property is the result of the experiment, and isn't a limitation of the particle. $\endgroup$ – MaxW Nov 20 '15 at 21:29

Actually, everything has wave-particle properties and is given by the deBroglie equation: $${\mathrm p}\lambda = h$$ where $\mathrm{p}$ is momentum (mv), $\lambda$ is wavelength and $h$ is known as the Plank constant ($6.626\cdot 10^{-34}\;\mathrm{J\cdot s}$).

As you can see as the mass of an object increases, the wavelength decreases. So in macroscopic objects that we an see, such as ball, its mass (therefore momentum) is so big compared to $h$ that the wavelength is really, really small, so we can't observe it. For light waves, it is the opposite. Due to their relatively large wavelength, they have a really small mass. However we can do experiments that show the particle nature of light. Such as the photoelectric effect which can only be explained by thinking of light as a particle rather than a wave.

Electrons which have a mass of $9.011\cdot 10^{-31}\;\mathrm{kg}$ are in between the two examples that I have given you. It turns out that their mass is perfect for their wave and particle nature to be observed. Protons are roughly 1840 times heavier than electrons, however we are also able to observe their dual nature.

The answer your second question is that they do exhibit these wave and particle properties at the same time. An electron can't simply decide to be a particle for a certain instant than decide to become a wave in the next moment. All objects exhibit their wave-particle properties at the same time.

  • $\begingroup$ The wave nature of neutron is used in diffraction experiments, see en.wikipedia.org/wiki/Neutron_diffraction $\endgroup$ – ssavec Sep 10 '15 at 13:23
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    $\begingroup$ @ssavec - It goes beyond that; "buckyballs" (C60) and much larger molecules have been shown to interfere with the right apparatus. See this old Nature News story. I've just sort of come to accept that the only reason "I am" where I think I am is that almost all of me can almost always be found where I expect to find me to well within experimental tolerances. (I barely notice the fuzziness around the edges, and, honestly, that's probably just my eyes showing their age.) $\endgroup$ – Stan Rogers Sep 10 '15 at 17:48

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