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Wikipedia article on deuterium says this:

The deuteron wavefunction must be antisymmetric if the isospin representation is used (since a proton and a neutron are not identical particles, the wavefunction need not be antisymmetric in general).

I wonder why does the wave function need to be antisymmetric when isospin representation is used. I assume that if two somehow different particles are exchanged the total wavefunction changes sign. Is it so? Why?

Thanks

liberias
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1 Answers1

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The neutron and proton may be viewed as the same particle - sometimes referred to as the nucleon. A proton is a "nucleon with the isospin up" and the neutron is a "nucleon with the isospin down". With this qualification, it's still true that nucleons are identical fermions, so their total wave function has to be antisymmetric.

In the simplest Ansatz, the total wave function is the tensor product of the isospin wave function; spin wave function; and orbital (spatial) wave function. The odd number of those has to be antisymmetric for the result to be antisymmetric. The (anti)symmetry of each factor is governed by the total isospin (0 antisymmetric or 1 symmetric); total spin (0 antisymmetric or 1 symmetric); orbital angular momentum (even means symmetric and odd means antisymmetric).

Luboš Motl
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