Is a Pseudo-Wavefunction Really a Mixed State?

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Discussion Overview

The discussion revolves around the nature of pseudo-wavefunctions in the context of pseudopotentials, specifically whether a pseudo-wavefunction can be considered a mixed state of the original Hamiltonian. The scope includes theoretical considerations and technical explanations related to quantum mechanics and computational methods in physics.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant suggests that the pseudo-wavefunction represents a mixed state of the original Hamiltonian, prompting curiosity about this perspective.
  • Another participant counters that pseudopotentials eliminate nodes near the core, leading to a situation where the pseudo-wavefunction resembles 3d states rather than being a mixed state.
  • A different participant argues that the pseudo-wavefunction can be expressed as a sum of core-states and valence states, scaled by their overlaps, referencing the OPW-method.
  • Another participant expresses skepticism about the completeness of the all-electron basis in representing the pseudo-wavefunction, questioning the validity of the overlap argument.

Areas of Agreement / Disagreement

Participants do not appear to reach a consensus, as there are competing views regarding the nature of the pseudo-wavefunction and its relationship to mixed states and all-electron bases.

Contextual Notes

There are unresolved questions regarding the completeness of the all-electron basis and the implications of overlap integrals in representing pseudo-wavefunctions.

Modey3
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Hello,

I'm studying pseudopotentials right now, and I had an epiphany that the pseudo-wavefunction is really mixed-state of the original Hamiltonian. Has anyone ever thought about a pseudo-wavefunction that way? Just curious.

modey3
 
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I'm don't think that's correct. Pseudopotentials remove nodes that are near the core, so a pseudopotential for Nb (say) will have 4d valence states, however the 4d states will not have a node near the core so they really will look like 3d states. I don't think you can accomplish elimination of a node by mixing states with n > 4.
 
kanato,

If you take the overlap integral between the pseduo-wavefunction and a particular all-electron valence and the core wavefunctions you get non-zero terms. This means that the pseudo wavefunction can be represented as a sum of core-states and the valence states each scaled by their overlaps with the pseduo-wavefunction. The OPW-method does this.
 
Sure, there's non-zero overlap, but I am unconvinced as to whether the all-electron basis is "complete enough" to represent the pseudo-wavefunction.
 

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