What is the operator ~X defined in terms of its spectral decomposition?
a) The operator ~X is defined as the generator of spatial translations.
b) The operator ~X is defined as the generator of temporal translations.
c) The operator ~X is defined as the position vector operator.
d) The operator ~X is defined as the momentum vector operator.
I - The operator ~X has a continuous spectrum.
II - The operator ~X and the operator ~P satisfy canonical commutation relations.
III - The eigenstates of the operator ~X are given by the expression e−i~x′~P/~|0X〉.
IV - The function of a wave ψ(~x′, t) is the component of the vector |ψ(t)〉 on the vector base |~x′〉.
a) I and II are correct.
b) II and III are correct.
c) III and IV are correct.
d) I and IV are correct.