Quantum properties of massive particles

Light is often thought of as a wave, but it has particle-like properties also: it is emitted and absorbed in discrete quanta that have a well-defined energy and momentum. By the same token, electrons and other massive objects (massive means having a non-zero mass --- it doesn't have to be large) are often thought of as particles; but they have wave-like properties as well. For example, a monoenergetic beam of electrons, neutrons or protons can make a diffraction pattern just like light. The wavelength of the beam is related to the momentum of the particles by the relation

The wavelength is known as the DeBroglie wavelength and is exactly the same relation as was used for photons. One could also use the relation E = hf, however the energy would include the rest energy, making the frequency so high that it does not enter the simple examples we will discuss here.

In principle, all objects, no matter how massive, have DeBroglie wavelengths. However, for macroscopic objects, the wavelength is so much smaller than the object's physical size the wave-like behavior goes unnoticed.


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