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The reason I think this might be possible is best explained by looking at a particle in an infinite square potential well. Its wavefunction is composed of two waves (or whatever you call them in complex math) of the same wavelength going in opposite directions, which is how the wavefunction can oscillate in place. I could see the same happening with more complex wavefunctions that could be a bunch of these stacked on top of each other.

Basically, if you took an eigenfunction out of its potential well and placed it in a space where the potential was the same everywhere, would it stay the same?

The question that is claimed to answer mine is talking about an expanding infinite square potential well. I'm talking about taking the wavefunction and putting it in open space. Perhaps someone can explain to me why the answer is the same in both cases.

Let me know if anything needs clarifying.

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  • $\begingroup$ Well, what happens when you plug the solution into the SE with the new flat potential? $\endgroup$
    – Qmechanic ♦
    Commented Oct 30, 2021 at 4:58
  • $\begingroup$ Wouldn't that take knowledge of extremely advanced calculus? $\endgroup$
    – zucculent
    Commented Nov 1, 2021 at 15:56
  • $\begingroup$ Regarding your edit: why do you think a potential well expanding to infinite width on both sides is any different from just becoming open space? $\endgroup$
    – Ruslan
    Commented Nov 3, 2021 at 19:31
  • $\begingroup$ I couldn't tell that the well was expanding to infinite width. $\endgroup$
    – zucculent
    Commented Nov 3, 2021 at 19:33

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