# Probability amplitudes, de Broglie and Schrödinger

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?

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.