For multibosonic systems, as I understand, the wave function must always be symmetric (antisymmetric for fermionic, which this question easily generalizes to).(adsbygoogle = window.adsbygoogle || []).push({});

But as far as I can see for N>2 you can easily construct alot of other wave functions which are symmetric rather than the one my book finds (which essentially is the slater determinant one with + instead of -),if you allow for the fact that each product only contains product of two wave functions.

Say for instance you have 3 particles with wavefunction a1, b2, c3

Then we could choose:

ψ = a1b2 + a2b1 + a1b3 + a3b1 + (combination of a and c, combination of b and c in the same way)

The wave function above is invariant under any switch between the number 1,2 and 3 (which will represent the three coordinate sets for our bosons).

Why is it then, that a wave function of this kind is not acceptable?

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# Symmetric wave functions

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