Is it possible to map quantum states of different physical (quantum) systems to the same Hilbert space? For example if I consider two different molecules in the ground state, may I represent them as kets in the same Hilbert space? I am not considering to construct a tensor product of their own Hilbert spaces like in the case of composite systems.
If I am not wrong, I recall that in S matrix scattering theory, different colliding particle are mapped to kets in the same Hilbert space.
If it is correct, may I think that a mixture state of a quantum system is a result of a statistical ensemble of states of different (quantum) physical systems?