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## Main Question or Discussion Point

I'm a QM noob/newb trying to understand the physical implication of a wave packet, in my mind it is something like this:

On the x axis there is displacement (vibration), probability on the y. I Imagine stretching and compressing the wave packet. When I stretch it out, the amplitude must decrease, as the total area must stay the same? As it stretches further and further it becomes closer to a line (being equally present along the trajectory?). So this equivalent to a constant massive particle speeding up? In reverse as something decreases in momentum, it's wave like character decreases as the wave packet becomes more localized, so it is easier to tell were it actually is. Increase it to infinity (which is of course impossible) and its position becomes completely defined, whist the probability of it being detected outside of its position becomes undefined, so we have no idea where it is going (momentum).

i.e. a normal wave has no position, because it continues to infinity, but we know it will oscillate the same forever. Yet, a wave pulse (packet) has a more specified definition, but it's oscillation changes (it's wave character dissipates), so we don't know how much momentum it really has.

And of course, how does this relate to the momentum of a wave? if the wave packet localizes, wont the wavelength get shorter, increasing momentum, thus being contradictory? Does the de Broglie momentum apply to all matter, and override the simple: p=mv? And p tends to infinity, wavelength tends to zero, so I'm guessing that relates to the constituent waves as producing a wave packet that is more confined means a wider distribution of wavelengths?

On the x axis there is displacement (vibration), probability on the y. I Imagine stretching and compressing the wave packet. When I stretch it out, the amplitude must decrease, as the total area must stay the same? As it stretches further and further it becomes closer to a line (being equally present along the trajectory?). So this equivalent to a constant massive particle speeding up? In reverse as something decreases in momentum, it's wave like character decreases as the wave packet becomes more localized, so it is easier to tell were it actually is. Increase it to infinity (which is of course impossible) and its position becomes completely defined, whist the probability of it being detected outside of its position becomes undefined, so we have no idea where it is going (momentum).

i.e. a normal wave has no position, because it continues to infinity, but we know it will oscillate the same forever. Yet, a wave pulse (packet) has a more specified definition, but it's oscillation changes (it's wave character dissipates), so we don't know how much momentum it really has.

And of course, how does this relate to the momentum of a wave? if the wave packet localizes, wont the wavelength get shorter, increasing momentum, thus being contradictory? Does the de Broglie momentum apply to all matter, and override the simple: p=mv? And p tends to infinity, wavelength tends to zero, so I'm guessing that relates to the constituent waves as producing a wave packet that is more confined means a wider distribution of wavelengths?