Chapter 3
Wave optics
To this point we have discussed the geometrical optics of charged
particles in electric and magnetic fields, based on relativistic classical mechanics. This fails to explain the important class of phenomena arising from diffraction and interference of matter waves.
A proper description begins with quantum mechanics.
This is perhaps best appreciated by considering the analogy with
light optics. Einstein’s original hypothesis in 1905 holds that the
electromagnetic field is quantized. As such, light propagates in
discrete energy packets called photons. Furthermore, acording to
a later hypothesis by Einstein, a single photon is endowed with
momentum p which satisfies
h
p = ,
(3.1)
λ
where h is Planck’s constant, given by h = 6.6261 × 10
−34 Joulesec, and λ is the wavelength.
A later hypothesis of de Broglie states that this same relationship between momentum and wavelength holds for a particle with
mass and charge. This indicates a close analogy between the dynamical motion of a charged particle and a photon. Both exhibit
particle- and wave-like behavior.
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Wave optics
To this point we have discussed the geometrical optics of charged
particles in electric and magnetic fields, based on relativistic classical mechanics. This fails to explain the important class of phenomena arising from diffraction and interference of matter waves.
A proper description begins with quantum mechanics.
This is perhaps best appreciated by considering the analogy with
light optics. Einstein’s original hypothesis in 1905 holds that the
electromagnetic field is quantized. As such, light propagates in
discrete energy packets called photons. Furthermore, acording to
a later hypothesis by Einstein, a single photon is endowed with
momentum p which satisfies
h
p = ,
(3.1)
λ
where h is Planck’s constant, given by h = 6.6261 × 10
−34 Joulesec, and λ is the wavelength.
A later hypothesis of de Broglie states that this same relationship between momentum and wavelength holds for a particle with
mass and charge. This indicates a close analogy between the dynamical motion of a charged particle and a photon. Both exhibit
particle- and wave-like behavior.
123