Conditions for quantised or continuous energies

  • #1

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?
 

Answers and Replies

  • #2
Dick
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How about a square well whose sides have finite potential instead of infinite? Can you explain why that would work?
 
  • #3
So it would have quantised energy inside the well (since it's confined) and continuous energies outside the well?
 
  • #4
Dick
Science Advisor
Homework Helper
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If you mean by 'in' that it has energy less than the wall energy, yes.
 

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