what are matter waves ?

In quantum mechanics, the concept of matter waves or de Broglie waves  reflects the wave–particle duality of matter.
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 total energy E (sum of its rest energy and the kinetic energy) of a particle.