De Broglie Wavelength
In quantum mechanics, the concept of matter waves or de Broglie waves reflects the wave–particle duality of matter. The theory was proposed by Louis de Broglie in 1924 in his PhD thesis. The de Broglie relations show that the wavelength is inversely proportional to the momentum of a particle and is also called de Broglie wavelength. Also the frequency of matter waves, as deduced by de Broglie, is directly proportional to the particle's total energy, i.e. the sum of particle's Kinetic energy and rest energy.
Propagation of de Broglie waves in 1d - real part of the complex amplitude is blue, imaginary part is green. The probability (shown as the colour opacity) of finding the particle at a given point x is spread out like a waveform, there is no definite position of the particle. As the amplitude increases above zero the curvature decreases, so the amplitude decreases again, and vice versa - the result is an alternating amplitude: a wave. Top: plane wave. Bottom:wave packet.
Source: wikipedia, NASA