Do Quantum Numbers Determine the Node Structure of Wavefunctions?

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Discussion Overview

The discussion revolves around the relationship between quantum numbers and the node structure of wavefunctions, particularly in the context of many-body systems. Participants explore whether ground state wavefunctions must have zero nodes and if there are general rules governing the number of nodes based on quantum numbers.

Discussion Character

  • Exploratory
  • Debate/contested
  • Technical explanation

Main Points Raised

  • Some participants propose that the ground state many-body wavefunction must have zero nodes.
  • Others suggest there is a general rule that the ground-state eigenfunction has the least number of modes among the set of eigenfunctions.
  • A later reply questions whether it is possible for the ground state to have a node.
  • Another participant mentions that for certain peculiar potentials, the ground state could indeed have nodes, citing examples from precolor quark models that had angular nodes to accommodate Fermi statistics.

Areas of Agreement / Disagreement

Participants express differing views on whether ground state wavefunctions can have nodes, indicating that multiple competing perspectives remain unresolved.

christianjb
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It seems likely- but is it true that the ground state many-body wf must have zero nodes?

Is there a general rule for the nodes as a fn of quantum numbers?
 
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christianjb said:
It seems likely- but is it true that the ground state many-body wf must have zero nodes?

Is there a general rule for the nodes as a fn of quantum numbers?

There is a general rule that the ground-state eigenfunction of a system must have the least number of modes in that set of eigenfunctions.
 
Surrealist said:
There is a general rule that the ground-state eigenfunction of a system must have the least number of modes in that set of eigenfunctions.

OK, but then it is possible for the ground state to have a node?
 
For some peculiar potentials, the ground state could have nodes.
Some precolor quark models had angular nodes to allow for Fermi statistics.
 

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