# Diffraction of matter waves

By considering the De Broglie wavelength of particles, we discover that matter can diffract if passed through openings with itself. This poses a variety of questions, namely

• Can matter waves interfere with light? For this, I'm pretty sure not, in the same way light does not diffract with sound waves as they operate with different mechanisms.

• Can matter waves of different types interfere with each other? For instance can a beam of electrons and a beam of protons display wave like properties combined? I'm not sure how distinctions can exist between the matter waves of electrons and protons, but I believe that there must be some fundamental difference between them.

• In the twin slit experiment, the matter waves involved in interference are most usefully considered as probability waves and their constructive /interference pattern produces a probability that the matter, say an electron, will be found at a particular place. If a photon of light is travelling directly towards the experiment, there is a probability that it may deflect (interfere with) the electron. This link physics.weber.edu/carroll/honors/duality.htm might be helpful to you.
– user81619
Commented May 22, 2015 at 10:17

Protons and electrons both obey the de Broglie hypothesis: wavelength = Planck constant / momentum. But protons do not act within the atom the same as electrons - they move in a tighter radius at higher speed. They have to be accelerated to reveal their wave nature, and as the momentum of a proton would be much greater than that of an electron at typical acceleration energies, the proton wavelength would be much smaller than an electron's.

A proton's mass is 1.672 * 10^-27 kg, or 938.273 MeV. An electron's mass is 9.109 * 10^-31 kg, or 0.511 MeV. Due to their different masses, they would have to be accelerated at different speeds to achieve the same wavelength. If it were possible to combine two differently accelerated beams, phase differences between them would have to be held constant during the period of observation, for a recognizable interference pattern to appear.

If it were not possible to combine beams of different acceleration, then different wavelengths require different widths of the slit for recognizable interference patterns, so it may not be possible for a slit to reveal interference for both protons and electrons. Also, as the wavelength of a particle tends toward zero, it acts more in a classical way, and the wave nature of the proton, with very short wavelengths, may not be very apparent. It's unlikely that a beam of protons would interfere with a beam of electrons.

A further consideration is that protons and electrons have opposite charge, so they would tend to collide and combine, rather than to pass through a slit as independent particles.

The wavelength of light (10^-9) is orders of magnitude longer than the wavelength of a proton (10^-15) at typical acceleration energies. I don't see how it would be possible for the matter wave of a proton to interfere with light waves.

Sort of a silly answer, but a bunch of protons, electrons, and neutrons bound together (i.e. an atom or molecule) can certainly diffract through a double slit. This has been taken to ridiculous extremes in recent years: witness the double-slit diffraction of C284H190F320N4S12, a molecule with 810 atoms and over 5000 electrons.

But if you're thinking about an experiment where you, say, shine an electron beam through one slit and a proton beam through another slit, then these two beams will not interfere with each other. On the level of QFT, an electron is really just an excitation of the "electron field" (a spinor field); and if we ignore the substructure of the proton, we can define a "proton field" in the same way. These two fields are different things, just as the "photon field" $A^\mu$ is distinct from the matter fields; and so long as we can neglect the interactions of these fields, we will get negligible interference between them.