- #1
Niles
- 1,866
- 0
Hi all.
This isn't a homework question, but something I thought about. When looking at a system of 2 fermions, we have that:
[tex]
\Psi(r_1,r_2)=-\Psi(r_2,r_1).
[/tex]
Now if we look at a 3 fermion system, then what is the demand for the waveequation? Does it have to be anti-symmetric when switching two of the particles or all three? And if it is all three, then in what order? I.e.:
[tex]
\Psi(r_1,r_2,r_3)=-\Psi(r_2,r_1,r_3) \qquad \text{or}\qquad \Psi(r_1,r_2,r_3)=-\Psi(r_3,r_1,r_3).
[/tex]
I hope you can shed some light on this. Thanks.
This isn't a homework question, but something I thought about. When looking at a system of 2 fermions, we have that:
[tex]
\Psi(r_1,r_2)=-\Psi(r_2,r_1).
[/tex]
Now if we look at a 3 fermion system, then what is the demand for the waveequation? Does it have to be anti-symmetric when switching two of the particles or all three? And if it is all three, then in what order? I.e.:
[tex]
\Psi(r_1,r_2,r_3)=-\Psi(r_2,r_1,r_3) \qquad \text{or}\qquad \Psi(r_1,r_2,r_3)=-\Psi(r_3,r_1,r_3).
[/tex]
I hope you can shed some light on this. Thanks.