- #1

Sciencemaster

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- TL;DR Summary
- If a particle is observed and its wave function collapsed, will its wave function spread out across space more quickly than before it was observed or than it would were it not observed?

For the sake of this question, I am primarily concerned with the position wave function. So, from my understanding, the wave function seems to 'collapse' to a few states apon measurement. We know this because, if the same particle is measured again shortly after this, it will generally remain in the same place (similar to what is described by Zeno's paradox). However, from what I have seen, it seems like the wave function generally spreads more quickly after measurement, which means that the likelihood of the particle being measured in the 'middle' decreases, and the probable locations of it being measured spread out. I think that this is due to the uncertainty in position becoming small enough that the uncertainty in momentum must increase to accommodate the Heisenberg Uncertainty Principle--which in turn causes the wave packet to spread more quickly, as there is some 'probability' that it moves more quickly in either direction, and there are more possible momenta--as the measurement--and thus collapse--of the wavefunction makes the wave packet 'tighter' and makes the uncertainty in position smaller. Is this correct that the wave function of a particle will spread more quickly after it is measured than it does in the previous state (assuming that the measurement decreases the uncertainty in position)? If so, can modern measurement devices measure a particle to the point that this occurs? Does this occur due to an increase in deviation of the momentum probability distribution? Will the wave spread faster if a wave packet is 'tighter' when the scenario starts, but is not measured?

A good way of visualizing this idea is through this PHET simulation I came across online: https://phet.colorado.edu/en/simulation/quantum-tunneling.

Notice that the wave packet spreads out more quickly after it is collapsed than it does before it is, or than it does after the same amount of time if you don't collapse it. Is this accurate to our understanding in real life (As in, experimental observation)?

Side question, is this simulation reasonably accurate to how a wave packet works in real life?

A good way of visualizing this idea is through this PHET simulation I came across online: https://phet.colorado.edu/en/simulation/quantum-tunneling.

Notice that the wave packet spreads out more quickly after it is collapsed than it does before it is, or than it does after the same amount of time if you don't collapse it. Is this accurate to our understanding in real life (As in, experimental observation)?

Side question, is this simulation reasonably accurate to how a wave packet works in real life?