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I'm not asking whether two fermions of different types can occupy the same quantum state, cf. the Pauli exclusion principle. I'm asking whether fermions of different types would have the same options available if you had one in at a time. An example of what I mean is the fact that muons will occupy much smaller orbitals around nuclei than electrons will. In this case, electrons and muons don't seem to have the same quantum states available for them around a nucleus. Is this the case with any two fermion types?

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The difference in the bound states of electrons or muons and a nucleus originates from their different masses (muons are a lot heavier than electrons). Because the Hamiltonian of the problem depends on the mass, the energy eigenvalues do as well.

In general, fermions (or any two particles) will be able to occupy the same state if all their properties which enter the Hamiltonian are the same. For example, a spin-up and a spin-down electron have the same states in an atom as long as there is no magnetic field. As soon as a magnetic field is switched on, this degeneracy disappears, because the spins have an energy in the magnetic field which depends on their direction.

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