For a particle moving in a potential V(x), what are plausible forms of V(x) that give:
(i) entirely continuous,
(iii) both continuous and quantised
energies of the particle? Sketch, with justification, the forms of V(x) for each of these 3 cases.
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?