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De Broglie Wave Revision Notes

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19.4De Broglie Wave


In these revision notes for De Broglie Wave, we cover the following key points:

  • Can particles manifest wave behavior?
  • What is the relationship between energy of particle and its wavelength?
  • What is the De Broglie relation?
  • How the wavelength of a particle is related to its momentum?
  • What is the wavelength of electron comparable with?
  • What is the probability approach used for the De Broglie wave?
  • Is the particle-wave nature specific only for EM waves or it extends in other elements of the universe?

De Broglie Wave Revision Notes

Louis De Broglie supported the idea that "moving electrons have a corresponding kind of wave associated, whose wavelength is determined only by the electron momentum." In this way, he postulated the relationship between its wavelength and the impulse of electron, that is

λ = h/p

De Broglie relation represents a generalization of the particle-wave dualism.

The electron's wavelength is comparable to wavelengths of X-radiation of EM waves. This is the reason why electronic beams incident on crystals gives diffract visibly and produce patterns similar to those produced by X-rays. In this sense, expressions like "electron has a wave nature" or "electron manifests wave behavior" are very meaningful.

The phenomena of interference and diffraction of electrons are well explained and interpreted through probability pictures, similar to the method used to figure out photons. Given this, we can assert that: "De Broglie wave for electrons (as well as for other matter particles) is a probability wave."

The intensity I of De Broglie wave as well as the square of its amplitude a, represent the probability for the electron to strike a specific point of the screen. In other words, it is not taken for granted that an electron will hit a specific point of the screen; everything is just probability (chance for an event to occur).

For electrons (and other material particles):

I∝ a2

the probability to detect the electron at a specific point

For photons:

I∝ a2

the probability to detect the photon at a specific point

Therefore, as a conclusion, we can say:

  1. The particle-wave dualistic nature is a fundamental feature for both EM radiation and matter.
  2. The particle-wave dualism is universal; it includes the entire universe.

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