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Can de Broglie wavelength of a particle be smaller than its size?

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Yes, that is possible. The momentum of the particle dictates its de-Broglie wavelength, not its dimension. Hence, large particles often have a smaller de-Broglie wavelength than their dimension. It has also been experimentally observed in this paper (more papers exist but this one deals with very large particles).

There is another interesting discussion on the validity of computing the de-Broglie wavelength of a macroscopic object on PhysicsSE.

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  • $\begingroup$ A very common and well studied example is nuclear fusion of heavy ions. The de Broglie wavelength corresponds to the center of mass motion. $\endgroup$ – user4552 Apr 16 '18 at 12:53

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