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I've been reading this question and the answers it received, and I still have some unresolved questions.

It is common to use the semiclassical approximation in describing charge carrier transport in semiconductors (for example, see Ashcroft & Mermin chap. 29). Wavepackets are combinations of momentum eigenstates that give some localization to a particle (electron or hole) within the limits of the HUP. This is helpful in view of the importance of position and distance in semiconductor device design (e.g., depletion regions, base layer widths in BJTs, FET channels, etc.). It is also noteworthy that many simplified diagrams of p-n junctions have an x-axis.

Basically, my question is this: When we discuss occupied states in a semiclassical context, does this only refer to energy/momentum eigenstates (delocalized, without reference to position), or does it mean instead that the energy states in a particular x,y,z region are occupied?

In the case of depletion regions, no (or very few) electrons are available in the conduction band, and no (or very few) holes are available in the valence band because of recombination. To me that seems like states that are occupied (or unoccupied) locally.

Dave
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    It’s both. In the classical limit, Heisenberg uncertainty is negligible, so you can have fairly well-defined position and momentum simultaneously. – knzhou Sep 20 '22 at 20:45
  • @knzhou Ahh okay. Is Pauli exclusion still dictating how electrons behave semiclassically? – Dave Sep 20 '22 at 22:45
  • Yes. Pauli exclusion is a quantum effect that can't really be ignored and is a key ingredient in the semi classical model (via Fermi-Dirac statistics). – lnmaurer Sep 23 '22 at 14:42
  • @inmaurer I've been reading Ashcroft chapter 12 further and came across mention of six-dimensional rk space. Could a semi-classical state simply be described as a point (or small region) in such a six-dimensional space? Apologies if it's an obvious question, my background is electronics not quantum physics – Dave Oct 04 '22 at 17:31

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