Regarding a potential well that is proportional to -1/|x|, are the amount of possible energy levels finite or infinite? (The potential well is narrow in the middle and approaches a horizontal asymptote as you leave the middle, like the shape of a tornado).(adsbygoogle = window.adsbygoogle || []).push({});

I figured it would be infinite, because the well gets infinitely wide before the horizontal asymptote so that energy levels of any "length" could fit between the walls. But It doesn't really make sense if there's a finite max potential energy (~horizontal asymptote) and the professor said there was a flaw in my reasoning.

I thought about it for a while and couldn't seem to find the explanation.

Lastly, two quick questions: is it correct to say that as you approach the horizontal asymptote, the energy levels get infinitely close together? I'm guessing it's wrong because that implies an infinite amount of energy levels. And can the -1/|x| potential well be used to describe the hydrogen atom?

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# Characteristics of a Potential Well that is Proportional to -1/|x|

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