= de Broglie wavelength
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{title2=$\lambda=h/p$}
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The <de Broglie wavelength> is the distance over which a <matter wave> accumulates one full spatial <quantum phase> cycle in its propagation direction:
$$
\lambda=\frac{h}{|\mathbf p|}=\frac{2\pi}{|\mathbf k|},\qquad \mathbf p=\hbar\mathbf k,\qquad \hbar=\frac{h}{2\pi}.
$$
Here $h$ is the <Planck constant>, $\mathbf p$ is the <momentum>, and $\mathbf k$ is the angular <wavevector>. The scalar $p$ in $\lambda=h/p$ means the positive <momentum> magnitude, not a signed component. Reversing a <momentum> reverses the <wavevector> without making the <wavelength> negative. At zero <momentum> there is no finite spatial phase period: the limiting <wavelength> diverges.
This relation makes microscopic <diffraction> accessible with particles: increasing the <momentum> shortens the <wavelength> until it is comparable with the spacings in a <crystal scattering> problem. The <electron accelerating-voltage wavelength> gives a practical way to tune this scale, while the <Davisson–Germer experiment> tests it by comparing <electron diffraction> directions with independently known crystal geometry. The same relation applies to neutral particles in a <neutron interferometer>; <electric charge> is not a requirement for a <matter wave>.
The <wavelength> belongs to the <wavefunction>, not to a sinusoidal path of a particle. A <free-particle momentum convention> makes the distinction especially clear: a <plane wave> has a rotating complex <quantum phase> but a constant <probability density>. A localized <wave packet> contains a range of <momenta> and therefore generally has a range of <wavelengths>, rather than one exact spatial period.
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