# Probability amplitudes, de Broglie and Schrödinger

## Main Question or Discussion Point

What is the relationship between the "matter waves" described by de Broglie, the probability amplitude function and Schrödinger's wave equation?

"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."

"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?

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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 $$|E(x)|^2$$ as the intensity of the wave.