The wave-particle duality, observations and probability

The constant Ac = 2.425 pm is called the Compton wavelength of the electron. The wavelength shift given by Eq. (1.10) can be easily reproduced theoretically if the interaction between the radiation and the electron is considered as a collision between two particles in which the energy and the linear momentum are conserved (conservation of momentum in the incident direction and in the direction perpendicular to it). These particles are a photon of energy hv and linear momentum p = hvlc=hlX and a stationary electron of mass m which acquires velocity v (Fig. 1.2). It is then found 

Equation (1.5) establishes a bridge between a description of fight as an (electromagnetic) wave of frequency v and as a beam of -q energy particles. If phenomena related to time averages, such as diffraction and interference, can be easily interpreted in terms of waves, other phenomena, involving a one-to-one relation such as the photoelectric and the Compton effects, require a description based on corpuscular attributes. This wave-particle duality reflects the use of one or the other description depending on the experiment performed, while no experiment exists which exhibits both aspects of the duality simultaneously. 

The form p = hvlc = hlX for the linear momentum of a photon can be obtained by combining the expression for the energy of a photon E=hv and the expression =mphC which defines the relativistic mass of the photon, mph, provided that the linear momentum of a photon is made equal to WphC by analogy with the classical expression jv for the hnear momentum of a particle. 

Strongly influenced by the interpretation of the Compton effect, the French physicist Louis Victor, Prince de Broghe (1892-1987, 1929 Nobel laureate in Physics), suggested in his doctoral thesis in 1924 that the wave-particle duahty for photons could be extended to any particle of momentum p = mv which, somehow, would then have a wavelength - the de Broglie wavelength - associated with it and given by 

Indeed, considering that photons are rather peculiar particles in that they have zero rest mass and can exist only when travelhng at the speed of fight, it seems reasonable that the wave associated with the motion of any particle should become more and more apparent as the mass decreases, rather than the wave coming into existence suddenly when the rest mass vanishes. 

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