# [Physics] Why does the wavelength of a particle go down with higher velocity

dispersionquantum mechanicsvelocitywave-particle-dualitywavelength

In mechanical waves, the wavelength increases with a higher velocity.
λ = v / f.
And the wavelength in particles lower with a higher velocity.
λ = h / mv.

This is deceptive:

$λ = v / f$ for waves that transfer energy with a fixed velocity v in a medium. This is a constant for the medium for all waves (acoustic, even light which is in vacuum with a constant c velocity)

Suggested by De Broglie in about 1923, the path to the wavelength expression for a particle is by analogy to the momentum of a photon.

The appropriate formula for particles in analogy with the photon is

the de Broglie hypothesis which can be derived from the postulates of quantum mechanics. . The velocity represented by the momentum , $p$, is variable dependent on the condition of the particle. The wave nature of the particle is a probability wave, not a mass or energy wave.

A single particle does not register as a wave, it is always a point in (x,y,z,t). An accumulation of particles with the same boundary conditions will show wave behavior in the probability distribution. See this answer to see how one measures a probability distribution for a particle.