Do Quantum Numbers Determine the Node Structure of Wavefunctions?

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The discussion centers on whether quantum numbers determine the node structure of wavefunctions, particularly regarding the ground state many-body wavefunction. It is generally accepted that the ground-state eigenfunction must have the least number of nodes among its eigenfunctions. However, there are exceptions where the ground state can possess nodes, especially in unique potential scenarios. Some models, like precolor quark models, demonstrate that angular nodes can exist to accommodate Fermi statistics. Overall, while a zero-node ground state is typical, it is not an absolute rule.
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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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