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de_broglie_matter_waves [2021/02/03 21:58] – [1.v.3 Experimental Confirmation of de Broglie's Hypothesis] adminde_broglie_matter_waves [2022/10/13 18:00] (current) – [1.v.1 de Broglie Wavelength and Wave Vector] admin
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 ====== 1.v.1 de Broglie Wavelength and Wave Vector ====== ====== 1.v.1 de Broglie Wavelength and Wave Vector ======
  
-The photoelectric effect and Compton scattering show that electromagnetic waves sometimes exhibit particle-like properties.  In 1923, de Broglie proposed that matter, which we normally think of as made up of particles like electrons, protons and neutrons, should have wave-like properties.  In other words, //everything// has both wave- and particle-like properties.+The photoelectric effect and Compton scattering show that electromagnetic waves sometimes exhibit particle-like properties.  In 1923, Louis de Broglie proposed that matter, which we normally think of as made up of particles like electrons, protons and neutrons, should have wave-like properties.  In other words, //everything// has both wave- and particle-like properties.
  
 Obviously, electromagnetic radiation does behave like a wave in many circumstances and matter behaves as if it were made up like particles in many circumstances, i.e., all circumstances where classical physics provides an adequate account.  Therefore, whether a system exhibits wave-like or particle-like properties depends on the experiment that we are doing.  This is known as //**wave-particle duality**//. Obviously, electromagnetic radiation does behave like a wave in many circumstances and matter behaves as if it were made up like particles in many circumstances, i.e., all circumstances where classical physics provides an adequate account.  Therefore, whether a system exhibits wave-like or particle-like properties depends on the experiment that we are doing.  This is known as //**wave-particle duality**//.
  
-For a photon, we have $E = pc$ and the quantum postulate says that $E = h\nu$.  Combining these gives $p = h\nu /c = h/\lambda$, or $\lambda = h/p$.+For a photon, we have \(E = pc\) and the quantum postulate says that $E = h\nu$.  Combining these gives $p = h\nu /c = h/\lambda$, or $\lambda = h/p$.
  
 de Broglie proposed that the same relation should hold for matter particles, so a matter particle with momentum $p$ is associated with a wave of wavelength de Broglie proposed that the same relation should hold for matter particles, so a matter particle with momentum $p$ is associated with a wave of wavelength
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 ====== 1.v.2 de Broglie Wavelength of the Electron ====== ====== 1.v.2 de Broglie Wavelength of the Electron ======
  
-Before computing the de Broglie wavelength of the electron, a word on units.  Since Planck's constant and the masses of elementary particles are so small, the typical masses and energy scales involved in quantum mechanics are very small.  Therefore, it is common to measure masses and energies in //**electron volts ($\text{eV}$)**// rather than the SI unit Joules ($\text{J}$).+Before computing the de Broglie wavelength of the electron, a word on units.  Since Planck's constant and the masses of elementary particles are so small, the typical masses and energy scales involved in quantum mechanics are very small.  Therefore, it is common to measure masses and energies in //**electron volts**// ($\text{eV}$) rather than the SI unit Joules ($\text{J}$).
  
 The electron volt is a unit of energy, defined to be the change in electric potential energy of an electron as it moves across a potential difference of $1\,\text{V}$.  Thus, the conversion factor is The electron volt is a unit of energy, defined to be the change in electric potential energy of an electron as it moves across a potential difference of $1\,\text{V}$.  Thus, the conversion factor is
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 This is a pretty good agreement with the theoretical de Broglie wavelength of $0.167\,\text{nm}.$ This is a pretty good agreement with the theoretical de Broglie wavelength of $0.167\,\text{nm}.$
  
-Many other matter interference experiments have been conducted since the Davisson-Germer experiments.  It is now possible to perform the double-slit experiment with electron beams and the size of particles we can detect interference with has been gradually increasing.  For example, in 1999 the double-slit experiment was performed with carbon-60 molecules (buckyballs).+Many other matter interference experiments have been conducted since the Davisson-Germer experiment.  It is now possible to perform the double-slit experiment with electron beams and the size of particles we can detect interference with has been gradually increasing.  For example, in 1999 the double-slit experiment was performed with carbon-60 molecules (buckyballs).
 ====== 1.v.4 de Broglie Matter Waves ====== ====== 1.v.4 de Broglie Matter Waves ======