Note: I am going to use |a> <a| to denote ket and bra vectors
The components of the state of a system| ω1> in some basis |δ1>, |δ2>, |δ3> are given by
<δ1|ω1> = i/sqrt(3), <δ2|ω1> = sqrt(2/3), <δ3|ω1> = 0
Find the probability of finding the system in the state |ω2> whose components in the same basis are
<δ1|ω2> = (1+i)/sqrt(3), <δ2|ω2> = sqrt(1/6), <δ3|ω2> = sqrt(1/6)
The Attempt at a Solution
I am actually rather confused just on how to start this problem. I am more familiar with the examples where I am given the matricies of observable and the components of a state function. Then I know that you have to find the eigenvectors corresponding to an eigenvalue and to use those to find the probability of an energy level.
So here we are dealing with two states being represented in a basis and I don't know how to weed through this to get any real information on either of these states or the basis.
Thank you for reading!