I was watching a lecture video from MITx $^\dagger$ by professor Barton Zwiebach. He proved a pretty cool theorem "every attractive 1-dimensional potential has a bound state"; however, that only holds in 1-dimension, and the theorem doesn't hold in 3-dimension.
Then I was left wondering:
How do we generate any results only valid in 1D/2D to our 3D world (I mean, after all, our world is 3D) ? Or how this theorem predicts anything in our real world such that we can test it experimentally?
I am a total newbie in experiment, if this question sounds silly to you, I am sorry!
I was thinking if an electron being constraint on a very thin plate would work. But I am not so sure, say, what about a curved - but super thin - plate? Does it counts 1D? or 3D?
$\dagger$: The course's website here. Which requires you have a EdX ID(free) to view the material.