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Perturbed (Curved) Square Well Potentials

Widdekind
in Quantum Theory

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What happens, to the Energy levels, of 1D potentials, when they are warped ? Do the Energies increase, or decrease ?

 

curvedsquarewellpotenti.jpg

I am not sure how you have orientated your diagrams. The potential needs to be single valued.

 

You may think about the infinite square well || and a curved one a bit like \ / (still going off to infinity) with the same width at V=0. See if you can come up with a simple argument to predict what happens to the states.

  • Author

I don't mean a spatially widening potential, but one which is warped, 'bowed',

 

|| ---> \\

||
........
||

||
.......
//

  • Author

What about an annular, ring-shaped potential (e.g. Cooper Pairs, in a ring-shaped super-conductor) ? How would the 1S, non-rotating, m=0 state compare, with the corresponding, un-perturbed potential ?

Edited by Widdekind

What about an annular, ring-shaped potential (e.g. Cooper Pairs, in a ring-shaped super-conductor) ? How would the 1S, non-rotating, m=0 state compare, with the corresponding, un-perturbed potential ?

 

I don't know, but this is not a one dimensional problem, right?

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