Node and Nodless wavefunction?

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Discussion Overview

The discussion revolves around the concepts of nodes and nodeless wavefunctions, particularly in the context of pseudopotentials. Participants explore the definitions and implications of these terms, seeking clarification on their meanings and applications.

Discussion Character

  • Conceptual clarification, Technical explanation

Main Points Raised

  • One participant asks for clarification on the meanings of "nodes" and "nodeless wavefunctions."
  • Another participant references the concepts of "nodes" and "antinodes" in standing waves, suggesting a foundational understanding of wave phenomena.
  • A participant acknowledges their familiarity with the terms but expresses confusion regarding the concept of nodeless wavefunctions in the context of pseudopotentials.
  • It is noted that in the context of pseudopotentials, "nodeless" refers specifically to the absence of radial nodes in one-particle basis functions, while angular nodes related to spherical harmonics remain present.

Areas of Agreement / Disagreement

The discussion does not reach a consensus, as participants express varying levels of understanding and confusion regarding the concepts of nodes and nodeless wavefunctions.

Contextual Notes

Participants highlight that the definition of "nodeless" is context-dependent, particularly in relation to the specific characteristics of pseudopotentials and the treatment of angular versus radial nodes.

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Node and Nodless wavefunction?

What means Node and nodeless wave functions?

Nawzad A.
 
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Do you know what "nodes" and "antinodes" are in standing waves?

Zz.
 


ZapperZ said:
Do you know what "nodes" and "antinodes" are in standing waves?

Zz.

Yes I know that , I am reading about pseudopotentials and I had faced that ( nodless wavefunctions) but I couldn't imagine how they are?!
 


new_986 said:
Yes I know that , I am reading about pseudopotentials and I had faced that ( nodless wavefunctions) but I couldn't imagine how they are?!
Note that in the context of pseudopotentials "nodeless" means "without /radial/ nodes" (in the one-particle basis functions; and actually, not even that, only the nodes corresponding the the electrons which are actually absorbed in the ECP are removed). The wave function still maintains all the angular nodes which are resulting from the spherical harmonic perfactors of the atomic wave functions.
 

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