My understanding of the wave function is that it shows the probability of observing something like an electron at different positions in a given moment in time. basically the x axis is position and the y axis is the probability (or can be used to find the probability).
the book I’m reading, in describing the uncertainty principle, shows how a wave function localized at a single point has an immeasurable wavelength, and a wave function with repeating waves and a measureable wavelength has multiple different possible locations.
that makes sense to me, and i understand that the amplitude corresponds to location probability, what I don’t understand is how wavelength shows momentum/speed.
the book references work by de Broglie and his discovery that wavelength correlates to momentum, but that doesn’t seem intuitive or obvious. How can you calculate the probability of measuring a certain speed just by looking at the wave function?