The Matter is Also the Wave,
said de Broglie

The Compton effect gives clear proof that electromagnetic emission sometimes can have particle features.
After Einstein we can ascribe mass to photon since it should be valid according to energy and mass equivalence:

E = m · c2 = hν | ® | m = hν/c² m = h/cλ

c = ν ·λ

A photon has an impulse

p = m · c = (h/cλ)· c

p = h/l

Experiments prove particle features of light. The emission wave characteristics were known according to interference and diffraction experiments. Louis de Broglie considered in 1924 that electrons and protons (and all other particles together with them) can behave like waves. It was proved by electron diffraction and interference experiments in 1927.

According to de Broglie one can write down:

Photon | Particle with mass m = m0/[1 − (v/c)2]½
p = | h/λ | = m · v | ® | λ = h/mv
E = | hν | = m · c2 | ® | ν = mc²/h

Focusing from Helium

Light can be diffracted according to Fresnel focusing. It can also be done with Helium atoms when using especially thin slit.

Fig.1: Scanning electron microscope picture of the Fresnel zone plate used to focus helium atoms. The plate has 128 zones and was produced by Heidenhain GmbH, Traunreut, Germany. It is made from a 0.5 µm gold foil; the radius of the innermost zone is 9 µm and the width of the fines ring is 0.4 µm.

The diffraction experiment with Helium atoms was carried out by group Toennies (Goettingen). They used the following scheme (Fig.2) in order to send cooled and parallel He-beam on the grating (Fig.3). The diffracted He-atoms were detected using mass spectrometer. The observed He-atoms diffraction (Fig. 4) directly corresponds to the expected diffraction after de Broglie. At the same time, it is clear that wave features of matter is also valid for compound systems rather than only for elementary particle. Another group of scientists have managed to obtain results from diffraction of Fullerens on the double slit.

Fig.2: Scientists measured diffraction of He-atoms using this apparatus.

Fig.3: One can see diffraction grating here through which He-atoms fly in order to form diffraction image. One can obtain its sizes from the left picture. Right picture shows form and production of such grating.

Fig.4: He-atoms signal after passing through mass spectrometer and being detected. The represented spatial distribution directly corresponds to that of de Broglie prediction. It's immediately clear that not only elementary particles behave reveal wave features but it is also true for compound systems.