# Baryon quark model: just a question

## Main Question or Discussion Point

I'm in trouble on answer to this question: "Wich is the (most probable) simmetry of the spatial part of the wavefunction for the lightest baryons? Why?"

I know that the spatial and spin parts of a baryon wavefunction must be simmetric under an interchange of any two quarks (this is an assumption on the quark static model, at least for the lightest baryons: the Pauli principle is not violated because there's the colour degree of freedom: to be "colourless" a baryon must be antysimmetric on the colour degree of freedom, so his "total" wavefunction results antysimmetric), and i also know that the spatial part in the lightest baryons has l=0, but i'm not able to motivate that answer exactly.

What i am forgetting?
Someone can help me?

Sorry for my english.

## Answers and Replies

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Meir Achuz
Science Advisor
Homework Helper
Gold Member
The lowest energy state of any system generally has no nodes.
Nodes introduce more curvature into the wave function which increases the energy. This makes the state with no internal or total orbital angular momentum the ground state.

The lowest energy state of any system generally has no nodes.
Nodes introduce more curvature into the wave function which increases the energy. This makes the state with no internal or total orbital angular momentum the ground state.

Then, talking about simmetry of the spatial part of the wavefunction, it's a spherical one, the most probably?

Thank you.

Meir Achuz
Science Advisor
Homework Helper
Gold Member
It is a three body wave function. While it has no angular momentum, it need not be completly spherical. That is, the distance between the two u quarks in a proton can be larger than that between a u land d quari.