I am just starting reading some quantum stuff. There of course be many questions here and there. One thing comes to bother me now that it seems QM are treating this "state" in either momentum or position representation, if leave alone spin space. It seems to treat "momentum" and "position" as two basises in that both can span the complete Hilbert space and a unitary tranformation is used to translate the two basis. I vision now the Hilbert space can be constructed with a intertwining "momentum" and "position" not exactly as a direct sum or product; they might not be orthogonal to each others but either one will not be able to span the whole Hilbert space. Did I misunderstand QM at all?