I know about symmetry and antisymmetry and so on, but a thought that I had never considered just hit me. If we had two fermions in the triplet symmetric spin state and hence therefore an antisymmetric spatial state, for example a harmonic oscillator in the first excited state must be one in state n and one in k:(adsbygoogle = window.adsbygoogle || []).push({});

psi = 1/(sqr root 2)( n1k2 - n2k1 )

But this wavefunction is clearly different from

psi = 1/(sqr root 2)( n2k1 - n1k2 )

Clearly it is just the exchange operator applied to the wave function, i can see that the expectation values will always be the same, so can you just choose how you order these and in which order they go?

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# Symmetry of Spatial Wavefunctions

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