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 Quote by betel It does not make sense to act with a single state ket $$\langle a|$$ on a tensor product state, unless a itself represents a tensor product state. In Other words to calculate the action you need both ket and bra to be in the same basis. So either you have to write a in the 2 particle Hilbertspace or you have to convert the compound system.
I see. I'll try doing that then. Thanks.