Hello there. I am a 2nd year uni student studying chemistry. I have a paper in a few weeks on the foundations of physical chemistry. I am having a problem with some quetions and would appreciate any help. Thank you to any who help. 1.Can the expectation value of the rotational angular momentum of a diatomic molecule be used to predict what value will be obtained experimentally if the rotational angular momentum of a single molecule is measure only once? Justify. My answer: The measurement of the observable <L> must be an eigenvalue to L(operator). L(operator)fn(x)=Lnfn(x) n=1,2,3... If the system is in an eigenstate of L(operator), the result gained must be of the observable L, that can only be of the particular eigenvalue characteristic of that eigenstate: say Ψ(x)=f7(x) then L=L7 Whereas if the system is not an eigenstate of L, the result of one measurement of a single diatomic can be in any one eigenstate of L(operator) but will be completely unpredictable: Ψ(x)≠fn(x) The eigenvalue is therefore completely unpredictable. The expectation value <L> would be given by: Integration over all space of the wavefunction(in all co-ordinates)*L(operator) d(all co-ordinates). Therefore <L> and the single measurement are unlikely to be the same.