They are telling you in part (b) to write ## O(t) ## in terms of the "eigenstates at t=0". ## O(t) ## is not required to be at ## t=0 ##. (the eigenstates at ## t=0 ##, is what they are referring to).b ## \\ ## Additional note: In the part you labeled "Answer: Unseen" , in the 3rd line, I think those should read ## u^*_m(x) ## and ## u_n(x) ##, without any ## t ## dependence.