de Broglie's Hypothesis

In 1926, Louis de Broglie hypothesized that massive particles have wave-like properties, and that the angular frequency, $\omega$, and wavenumber, ${\bf k}$, of a particle wave is related to the energy, $E$, and momentum, ${\bf p}$, of its constituent particles according to

$$E = \hbar\,\omega,$$ (4.8)

$${\bf p} =\hbar\,{\bf k}.$$ (4.9)

Obviously, these relations are the same as the relations between the angular frequency and wavenumber of an electromagnetic wave and the energy and momentum of its constituent photons. (See Section 4.1.2.) As discussed in Sections 4.1.6 and 4.1.7, relation (4.9) can be verified experimentally. On the other hand, relation (4.8) is adopted on the basis of an analogy drawn between massive particles and photons.