Perturbed (Curved) Square Well Potentials

[Widdekind]

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

 

[ajb]

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.

[Widdekind]

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

 

|| ---> \\

||

........

||

||

.......

//

[ajb]

I don't think that is allowed as it is not single valued.

[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 ?

Edited May 26, 2011 by Widdekind

[ajb]

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?