# Matter wave (1923, de Broglie hypothesis)

## de Broglie relations

Relates particle momentum and its wavelength, or equivalently, energy and frequency.
The wavelength relation is: $$λ=ph​ (1)$$ but since: $$v=λfE=pv (2)$$ the wavelength relation implies: $$fv​=ph​f=hvp​=hE​ (3)$$
Particle wavelength can be for example measured very directly on a double-slit experiment.
So if we take for example electrons of different speeds, we should be able to see the diffraction pattern change accordingly.

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