If light can be a particle, can a particle be a wave? De Broglie said yes: everything has a wavelength λ = h/p, shorter the more momentum it carries. An electron’s wave is big enough to diffract (and it does — that’s how electron microscopes work); a baseball’s wavelength is so absurdly tiny you never see it wave. Slide the momentum and watch the matter-wave shrink out of sight.
De Broglie (1924): a particle of momentum p has wavelength λ = h/p (h = Planck’s constant). More momentum — more mass or more speed — means a SHORTER wave. An electron (tiny mass) at modest speed has λ ~ 0.1–1 nm, comparable to atomic spacings, so it diffracts off crystals (Davisson–Germer 1927, confirming the hypothesis); a baseball has λ ~ 10⁻³⁴ m, unmeasurably small, so it never shows wave behaviour. A fail-loud self-check throws unless λ falls as p rises and the electron’s λ dwarfs the baseball’s. ◆ real quantum mechanics, node-verified.
The exact de Broglie relation with worked electron/baseball cases; a full treatment uses the relativistic p and the wavefunction’s phase/group velocities — the λ=h/p scaling and the classical/quantum divide are exact.