= Matter wave
{wiki}
A matter wave is the quantum wave associated with a material particle. Its phase can interfere after coherent paths recombine.
In the position representation, a <matter wave> is described by a <wavefunction>: a <complex number> <probability amplitude>, with detection probabilities given by the <Born rule>. A localized <wave packet> combines different <momenta>; its envelope can move while its individual <quantum phase> crests move at another speed. Neither curve is a literal mechanical oscillation of material along a particle's path. The <de Broglie phase harmony> explains the historical route to $\lambda=h/p$; the <relativistic matter-wave velocities> distinguish the two speeds. The <Davisson–Germer experiment> and the <Thomson electron transmission diffraction experiment> connect that spatial <quantum phase> to measured <electron diffraction>.
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