I am in the process of reading through The Theoretical Minimum. One of the processes it suggests is relating to orthogonal vectors, particularly representing the right (|R>) and left (|L>) spins. Common sense says they're orthogonal but I was wondering how exactly to represent the inner product. for |R> they gave the equation |R>=(1/sqrt(2))|U> +(1/sqrt(2))|D> where |U> and |D> represent up and down spins respectively. for |L> they gave the equation |L>=(1/sqrt(2))|U> -(1/sqrt(2))|D> where |U> and |D> represent the up and down states. My first intuition was to put them in vectors in order to find <R|L>. I used the coefficients to find the different parts of the vector. It came out correctly but I wanted to make sure I was using the correct process.