The ground state for two identical fermions in a box (in 1D) is given by:(adsbygoogle = window.adsbygoogle || []).push({});

[itex]\psi (x_{1},x_{2})_{12} = \frac{\sqrt{2}}{a}[sin(\pi x_{1}/a)sin(2\pi x_{2}/a) - sin(2\pi x_{1}/a)sin(\pi x_{2}/a)] [/itex]

The book I'm reading though says that this state is non degenerate, and that the next excited state is [itex]\psi_{13}[/itex]. My question is, why is the ground state not degenerate? Why can't you have either [itex]\psi_{12}[/itex] or [itex]\psi_{21}[/itex] which would have the same energy?

Thanks.

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Identical fermions in a box - degenerate states

**Physics Forums | Science Articles, Homework Help, Discussion**