 First consider the rest frame of the particle.In that case the frequency and wavenumber of the wave are related to the energy and momentum of the particles properties by

and

where m is the rest mass of the particle.This describes a wave of infinite wavelength and infinite phase velocity

The wave may be written as proportional to

This, however, is also the solution for a simple harmonic oscillator, which can be thought of as a clock in the rest frame of the particle.