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.

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# Identical fermions in a box - degenerate states

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