ABSTRACT
First, we consider a photon of light in a vacuum. The energy E of the photon is given by E = hυ (1.2) Here, υ is the frequency of the radiation in s-1. If Eq. 1.2 is combined with the well-known relation, then c = υλ0 (1.3) Here, c and λ0 are the speed and wavelength of light in vacuum, respectively. The result is that the energy of the photon is given by0= hcE l (1.4) There are some similarities between photons and electrons. Consider the propagation of photons in dielectrics material or in crystals. The basic equation describing the wavelength of light is= =h c
p l
(1.5) And the equation describing the wavelength of electrons is= =h h
p mv l (1.6) Then, we can compare the equation of motion between photons
and electrons that propagate in free space by the use of Maxwell’s equations for photons and Schrödinger’s equation for electrons. From Maxwell’s equations1× = DH
c t and –1× = BE c t (1.7)where B and H are the magnetic field and magnetic field strength, respectively, D is electric displacement field, and t is the time interval. For a plane wave 20. =E r k E r e (1.8)
where the solution is in the form of a photon plane wave: . .– – +0= +ik r t ik r tE E e ew w (1.9) And Schrödinger’s equation that allows us to calculate the energy of an electron is given by 2-. + ( ) ( )= ( )2 V r r E rm (1.10)
where the solution is in the form of an electron plane wave, given by .. – –= +ik r t ik r tc e ew w (1.11) The above equations have solutions in similar forms. Finally, we can conclude that free space propagation of both electrons and photons can be described by plane waves. There momentums are in the same analogues: =p k , where = 2k pl for a photon and =(2 / )k h mvp for an electron. The energy is E = pc for both photons and electrons. But, on the other hand, the propagation of light (or photon) is affected by the dielectric medium (refractive index), while the propagation of electrons is affected by Coulomb potential. Thus, we have some similarity in the properties of both photons and electrons.
