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Gaussian wave packets spread as the time passes, which means that as we go backwards in time they get more localized. Therefore, Gaussian wave packets introduce less uncertainty in the position as the we go backwards in time.

Are there wave functions (not necessarily Gaussian) in Nature that don't behave like this, i.e that don't get localized as we go backwards in time? If so, I think this would mean that the uncertainty they introduce in position doesn't necessarily increase with time (or decrease as we go backwards in time) as it does in the case of a typical Gaussian wave packet.

DanielSank
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Alex L
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    Coherent states have constant spread. – AccidentalFourierTransform Oct 15 '18 at 22:39
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    From what source did you get the impression that wavefunctions spread out over time? – Al Nejati Oct 15 '18 at 22:39
  • Are you asking about classical waves? – Lewis Miller Oct 15 '18 at 22:57
  • @AccidentalFourierTransform Do coherent states naturally exist in the nature (without a need to somehow produce them)? – Alex L Oct 15 '18 at 23:01
  • @LewisMiller I am talking about wavefuntions in quantum mechanics. – Alex L Oct 15 '18 at 23:02
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    QM is time reversible. – Keith McClary Oct 16 '18 at 02:28
  • @Ali From https://www.rp-photonics.com/coherent_states.html: “The output of a single-frequency laser well above threshold can approach a coherent state, if the long-term phase drift (related to the Schawlow–Townes linewidth) is disregarded.” – ZeroTheHero Oct 16 '18 at 02:28
  • @ZeroTheHero I was wondering if such states can be found in the nature without the need for producing them. The output of a laser is not something natural. – Alex L Oct 16 '18 at 02:40
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    @Ali where is the boundary between natural and not natural then? Is the $n$ excited state of a quantum harmonic oscillator natural? – ZeroTheHero Oct 16 '18 at 02:43
  • @Keith You mean the gaussian wavepacket can also spread as we go backwards in time? So it would be meaningless to say that wavefunction will get localized as we go backwards in time, in both time directions we can only see it spreading. Is that true? – Alex L Oct 16 '18 at 02:51
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    knzhou explains this here. – Keith McClary Oct 16 '18 at 03:01
  • @ZeroTheHero I meant particles which have existed forever, like electrons in atoms, photons, etc. I wanted to know if particles exist wavefunctions of which don't get localized no matter how much we go backwards in time. Coherent states have such wavefunctions, but can a particle in a coherent state have existed since the big bang? – Alex L Oct 16 '18 at 03:31
  • @Ali. If you didn't do this in your QM course, do it now. Superpose the ground state of the quantum oscillator on its first excited state. Observe Δx Δp oscillate in time. – Cosmas Zachos Oct 16 '18 at 21:55

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