= Solution
The <de Broglie hypothesis> associates a wave <phase> with a material particle. Its <momentum> and <energy> set
$$
\boxed{\lambda=\frac hp,\qquad \omega=\frac E\hbar,\qquad \mathbf k=\frac{\mathbf p}{\hbar}.}
$$
This is not a literal extended classical lump of matter oscillating at every point. A <wavefunction> gives amplitudes for measurements, and a localized particle is represented by a superposition of <momentum> waves. <Electron> <diffraction>, for example, exhibits <interference> at angles set by the same wavelength relation.
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