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Probability amplitudes, de Broglie and Schrödinger

  1. May 29, 2008 #1
    What is the relationship between the "matter waves" described by de Broglie, the probability amplitude function and Schrödinger's wave equation?

    I've read the following:

    "The wavelengths postulated by de Broglie to be associated with the motions of particles are in reality the wavelengths of the probability amplitudes or wave functions."

    I've also read:

    "What is a wave function? The short answer is that it is a probability amplitude, that also happens to solve Schrodinger’s equation."

    Are they all versions of the same thing?
  2. jcsd
  3. May 30, 2008 #2
    The wavefunction in one dimension is simply some function f(x) that solves Schroedinger's equation. It is called a "wave" function because the Schroedinger equation is mathematically similar to the so-called Wave Equation (Wikipedia explains).

    The probability amplitude is the square of the wavefunction. This is a postulate, so you'll have to remember it, or remember an analogy.

    In fact, it is analogous to the electric field (wave) E(x), since we think about [tex]|E(x)|^2[/tex] as the intensity of the wave.
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