Formation of a wavefunction, charge density

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Discussion Overview

The discussion revolves around the formation of wavefunctions and charge densities in the context of Density Functional Theory (DFT). Participants explore the implications of electron arrangements in potentials, the uniqueness of these arrangements, and potential opposing forces, as well as the role of entropy in this framework.

Discussion Character

  • Exploratory, Technical explanation, Debate/contested

Main Points Raised

  • One participant suggests that when electrons are placed into a potential, they arrange themselves into a unique wavefunction and charge density, questioning if there are forces opposing this arrangement beyond Coulombic forces.
  • Another participant asserts that DFT concerns the ground state of electrons, which is well-defined, implying that the original question may not be relevant to DFT.
  • A third participant references the Hohenberg–Kohn theorem, explaining that it establishes a uniqueness between density and potential, suggesting that the original question lacks clarity.
  • A fourth participant agrees that the question does not specifically pertain to DFT, indicating it relates more to information theory, while acknowledging familiarity with the Hohenberg-Kohn theorems.

Areas of Agreement / Disagreement

Participants express disagreement regarding the relevance and clarity of the initial question, with some asserting it does not pertain directly to DFT while others attempt to connect it to broader concepts. No consensus is reached on the implications of entropy or opposing forces.

Contextual Notes

The discussion highlights potential limitations in understanding the relationship between DFT, wavefunction uniqueness, and information theory, with some assumptions about the context of entropy remaining unresolved.

jajabinker
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I was studying Density functional theory, the premise of whose reasoning needs one to accept the phenomenon that when we place electrons into a potential, they "arrange" themselves into an unique wave function/charge density.

Are there any forces that oppose this arrangement? (other than the Columbic ones).

Anything we can say about entropy in this context?

Regards
 
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jajabinker said:
I was studying Density functional theory, the premise of whose reasoning needs one to accept the phenomenon that when we place electrons into a potential, they "arrange" themselves into an unique wave function/charge density.

Are there any forces that oppose this arrangement? (other than the Columbic ones).

Anything we can say about entropy in this context?
I'm not sure what you mean here. DFT concerns the ground state of the electrons, which is a very well defined state.
 
You're referring to the Hohenberg–Kohn theorem. It's just a uniqueness theorem - given some density [itex]n(\vec{r})[/itex] there is a unique potential corresponding to such a density.

Or, flipped around, given a specific potential, there is only one unique solution, in terms of the density, to the problem.

The rest of you question really doesn't make sense.
 
The question indeed does not make sense. It has nothing to do specifically with DFT, but more with information theory.

I am aware of the HK theorems.
 

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