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## 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?

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?

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?