# Fermions in bound states and their wavefunctions

1. Aug 10, 2009

### ZombieCat

Hello all,

This may be my very first post on Physics Forums. I am a 1st year physics grad student and need some help on something that's been bugging me. Suppose we have two spin half particles in a bound state. The total spin will either be 0 or 1. The spin 0 state, for example, would be symmetric (even parity right?) so it would need an antisymmetric spatial wavefunction to make the overall wavefunction antisymmetric since we have fermions? But then I thought the overall wavefunction may be symmetric because the total spin is that of a boson?

Rephrased, my question is this: would the total wavefunction have to be antisymmetric since we are dealing with fermions, or would it be symmetric since the total spin is that of a boson?
Which is it and why?

If we came along and didn't know that there were two fermions in there would we think it was a boson?

Does the fermions being in a bound state matter? What about the shape of the potential?

2. Aug 10, 2009

### tiny-tim

Welcome to PF!

Hello ZombieCat! Welcome to PF!
uhhh? did you use to be Schrodinger's cat?
It's symmetric because it is a boson …

a bound state of an even number of fermions is a boson.

That's why mesons are bosons, but protons and neutrons are fermions … they're two quarks and three quarks respectively!

3. Aug 10, 2009

### Avodyne

Sorry, wrong. The spin-0 state is antisymmetric, and the spin-1 state is symmetric.

4. Aug 11, 2009

### ZombieCat

Re: Welcome to PF!

Haha! I guess this zombie cat USED to be Schrodinger's cat, but is now the quantum mechanically undead. Thanks Tiny Tim!

As for the symmetry of the spin-0 state, (ud-du)/sqrt(2), I understand that the spins are opposed to make this happen and this state should be antisymmetric... I guess I'm getting confused about the difference between symmetry and parity, (-1)^L. Does this not apply here? Why not?