Electron in a well: energies are quantized or not?

[no_math_plz]

hi, I'm new on this forum, and I don't know english very well (sorry). maybe you can clarify me about this doubt. an electron in a well with infinite walls has a discrete set of energies, right? but if the length of the well is infinite, what can I say about energy state density? is it uniform (as energy state density of a free electron: that's reasonable, as a well of infinite length should simulate this situation), or not? calculus seems to avvalorate this second hypothesis...

 

[Dr Transport]

A finite well will have a finite number of allowed states associated with it and the energy density will be a series of delta functions.

 

[no_math_plz]

right, but in an infinite well such series becomes a continuous energy density because energy levels addensate: try to imagine...

 

[jtbell]

addensate?

 

[Dr Transport]

right, but in an infinite well such series becomes a continuous energy density because energy levels addensate: try to imagine...

The infinite well never has a continuous series of energy states, only discrete states..

I'm with jtbell, "addensate"?

 

[jtbell]

I think he's referring to an infinitely wide well, not an infinitely deep one.

 

[Ben Niehoff]

From the Latin roots, "addensate" should mean "to make more dense". Is your first language Italian, by any chance?

 

[no_math_plz]

yes, addensate=to make more dense! sorry, I thought this word exist in English. I'm referring to an infinitely wide well, not necessarily infinitely deep one: this should represent the free space. the question is: why energies in this case aren't distributed uniformly? for example, in a 3D-infinitely deep well energy density is an increasing function (right, energy states doesn't form a continuous set, but a dense set not uniformly distributed when width is infinite)