Dimensions of Angular and Radial Nodes

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Discussion Overview

The discussion revolves around the dimensions of radial and angular nodes in wavefunctions, specifically whether these nodes possess any thickness or are merely infinitesimal points in space. The scope includes theoretical considerations of wavefunctions in quantum mechanics.

Discussion Character

  • Exploratory, Technical explanation, Conceptual clarification

Main Points Raised

  • One participant asserts that radial and angular nodes are regions where the wavefunction is zero, questioning their dimensionality.
  • Another participant argues that these nodes are not points but rather subspaces, suggesting that they have size zero in a mathematical sense, while noting that introducing a non-zero probability density leads to a significant increase in size for realistic wavefunctions.
  • A third participant seeks clarification on the meaning of epsilon in this context.
  • A follow-up response explains that epsilon represents a non-zero real number, typically indicating a very small value related to the probability density of the wavefunction.

Areas of Agreement / Disagreement

The discussion features multiple competing views regarding the dimensionality of nodes, with no consensus reached on whether they are points or subspaces.

Contextual Notes

Participants reference mathematical concepts and the implications of introducing non-zero values for probability density, but the discussion does not resolve the underlying assumptions about the nature of nodes.

sams
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Radial and angular nodes are simply a region where the wavefunction is zero. But speaking about their dimensions, do they have any thickness or are they just an infinitesimal point in space without dimensions?

Thanks a lot!
 
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They are not points but subspaces. And size zero in math sense. As soon as you give an ##\epsilon>0## for the maximum probability density, that size shoots up to (near?) infinity for all realistic wavefunctions.
 
BvU said:
ϵ
What epsilon stands for?
 
A non-zero real number, as in 'for any probability ## \epsilon ## > 0 there is a volume > 0 where the wave function is < ##\sqrt \epsilon##'

usually ## \epsilon## means very small
 

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