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?