Usually, what is referred to as antihydrogen is uniquely defined: it is an antiatom made of one antiproton and one positron. However, in the same way we have several isotopes of each atom, we could have several isotopes of the antiatoms.
Does that mean the quantum functions are only serving the purpose of allowing states based on known subatomic particles? Or the other way around: What did we know first, positrons or the quantum functions that describe them?
This is on purpose: the summary comes at the end ;)
I know that now and I will not fall for it again:-)
The positron was discovered after the birth of quantum mechanics. In fact, antiparticles appeared naturally i the theory (the development of Klein-Gordon and Dirac equations) and physicists from that time were not understanding what they were.
To answer your question: The wave functions will be different for the different (anti)atomic species.
I hope it helps!
This topic is waaay above me, but actually yes, I can imagine something to what you've said. Thanks for that.
You are very welcome!