1. The problem statement, all variables and given/known data In quantum mechanics, what objects are the members of the vector space V? Give an example for the case of quantum mechanics of a member of the adjoint space V' and explain how members of V' enable us to predict the outcomes of experiments. 2. Relevant equations 3. The attempt at a solution In quantum mechanics, the members of the vector space V are wavefunctions that completely specify the quantum state of a system. If |ψ> is a member of a V, then its adjoint is the vector <ψ| which belongs to V'. When a member of V' is operated on the corresponding member of V to obtain a complex scalar, the square of the modulus of the complex scalar gives the probability distribution for the observable associated with the member of V.