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    $\begingroup$ How can this be compatible with relativity? Non-relativistic quantum mechanics isn’t supposed to be compatible with relativity. $\endgroup$ Commented Dec 2, 2024 at 17:52
  • $\begingroup$ That's fair, but i'm still confused about what happens in the second case, once somebody seemingly takes relativity into account $\endgroup$ Commented Dec 2, 2024 at 17:54
  • $\begingroup$ You are wading into muddy territory by taking the results of a time-independent problem (the potential is time independent for a particle in a box) and then trying to staple that result onto a time-dependent system in an ad hoc way. $\endgroup$ Commented Dec 2, 2024 at 17:57
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    $\begingroup$ Then why don't you consider what happens when you apply the "PW formalism" to this problem? $\endgroup$ Commented Dec 2, 2024 at 18:14
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    $\begingroup$ For the first scenario, the system starts in a very low energy state, if the wavelength of the particle is comparable to the size of a box that light takes a significant amount of time to cross. Because of the energy-time uncertainty principle $\Delta E \Delta t \gtrsim \hbar$, to measure the energy at all (and separate it from zero/no particle present) you're going to need to wait a very long time. Shaking the wall will change the energy of the system, but it'll take time to observe this. For your second scenario, I don't understand the "rotation"; you should try to write some equations. $\endgroup$ Commented Dec 2, 2024 at 19:59