Conditions for quantised or continuous energies

[aurora14421]

Homework Statement

For a particle moving in a potential V(x), what are plausible forms of V(x) that give:

(i) entirely continuous,

(ii)entirely quantised

(iii) both continuous and quantised

energies of the particle? Sketch, with justification, the forms of V(x) for each of these 3 cases.

Homework Equations

The Attempt at a Solution

(i) when the particle is free (V(x) is zero), the particles energies are continuous.

(ii) When the particle is in an infinite potential well, the energies are quantised.

(iii) I have no idea about this one. Can anyone help?

 

[Dick]

How about a square well whose sides have finite potential instead of infinite? Can you explain why that would work?

 

[aurora14421]

So it would have quantised energy inside the well (since it's confined) and continuous energies outside the well?

 

[Dick]

If you mean by 'in' that it has energy less than the wall energy, yes.