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For a two particle system in QM, if we have identical particles, which are fermions then we require that the overall wave function (position and spin) is antisymmetric and if the the particles are identical bosons then we require that overall wave function is symmetric, i.e.

$$\psi(r_{1},r_{2}) = A[\psi_{a}(r_{1})\psi_{b}(r_{2})\pm\psi_{b}(r_{1})\psi_{a}(r_{2}) ].$$

Question: But what are the rules when considering atoms. For example, helium or hydrogen seem to follow the fermion rules regarding when a wave function is symmetric or antisymmetric, that is the overall wave function should be antisymmetric. Do we follow the rules related to fermions for atoms as well since we have electrons involved? What is the basic motivation for these rules? I am just starting to learn about spin in QM, hence am using an introductory text.

Thanks.

Alex
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Indeed certain atoms are bosons and other atoms are fermions. Just to provide you with an example, Bose-Einstein condensates are often realized with ultracold bosonic atoms, such as $^4\mathrm{He}$ or Rubidium. Since these kinds of atoms are bosons, if you cool them down below a critical temperature, the wavefunctions of each single atom overlap and you can start talking about a macroscopic wavefunction: that's condensation!

The basic motivation is that every object is either a boson or a fermion, no matter if we are talking about a single electron, an hydrogen atom, a photon or an atom. Once you know what kind of particle you are dealing with, you automatically know which rule you have to follow.

AndreaPaco
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