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Louis de Broglie suggested that, if a particle like electron has momentum and wavelength associated with it (due to Planck's constant), then it might be a wave. The region where it exists are those where these waves interfere constructively. But these (electrons and protons) are the particles with mass and charge. Particles with which matter is made of. Matter which we can touch and feel and interact with on a macro level. How can matter thus exhibit a wave-like nature?

What is the nature of such a wave? (We consider it a wave just because the equation closely resembles a classical wave). Is it similar to the waves that occur in nature, or something entirely different?

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  • $\begingroup$ I’d turn it around on you a little and ask you to imagine how the stuff of everyday life can be “solid” on the micro level. If you could touch an electron, do you imagine it feeling hard? Smooth? If so, it implies you could cut it into smaller pieces of whatever you’re touching. You should see that whichever way you come at it, the descriptors we’re so used to simply can’t apply to whatever the basement level of reality is. So the ability to be somewhat undefined (neither true location nor momentum) seems no more strange than a detailed painting emerging from smudges of paint. $\endgroup$ – JPattarini Oct 2 '20 at 13:59
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In fact, it is the other way around. It is true that the behavior of matter, be it massive or massless, is governed by wave equations, such as Maxwell, Schroedinger, Klein-Gordon and Dirac. However, these equations describe the statistical behavior of matter, while matter itself consists of discrete particles.

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