What are Matter Waves?

Matter waves, also called de Broglie waves, are the wave-like nature of all matter, including the atoms that make up your body. One of the first and most important findings of quantum physics is that electrons have a dual wave-particle nature. It soon became apparent that all matter has this dual nature, but because conventional matter has a high momentum relative to electrons, the wavelength of the matter waves is very small, and in most cases barely noticeable. For instance, the wavelength of the matter that makes up a person is on the order of 10^{−35 meters}, far smaller than can be observed using current measurement technologies.

The concept of matter waves was first elucidated by French physicist Louis de Broglie, who was extending early theories proposed by Albert Einstein, Max Planck, and Neils Bohr. Bohr primarily studied the quantum behavior of hydrogen atoms, whereas de Broglie tried to extend these ideas to determine a wavelength equation for all matter. De Broglie came up with a theory and presented it in his 1924 PhD thesis, for which he was awarded the Nobel Prize for Physics in 1929. This was the first case where the Nobel Prize was awarded for a PhD thesis.

Equations known as the de Broglie relations describe the dual wave-particle nature of all matter. These relations state that the wavelength of a particle is inversely proportional to its momentum (mass times velocity) and its frequency is proportional to its kinetic energy, which is a frame-dependent (relative) value. Thus, particles with low momentum, such as electrons at room temperature, have a de Broglie wavelength of about 8 nanometers. Particles with even lower momentum, such as helium atoms at temperatures of only a few nanoKelvins, might have matter waves with wavelengths as long as a few microns. Under such unusual conditions, the realities of the quantum world are almost brought up into a the macroscale realm.

De Broglie's theories of matter waves were confirmed in 1927, when Bell Labs scientists Lester Germer and Clinton Davisson fired slow-moving electrons at a crystalline nickel target. The resulting diffraction pattern demonstrated the wave-like characteristics of the electrons, similar to those known to be displayed by photons such as those in x-rays. The matter waves were only able to be observed in this instance because the electrons used to produce them had very low momentum. Since 1927, the wave-like nature of various other elementary particles has been demonstrated empirically.