We know that a|n> = √n | √(n-1)> and a' |n> = √(n+1) | n + 1 > so, If we use this to find <n|a'a|n> it would be equal to n <n|a'a|n> = n Am I correct? I'm not really sure about my calculations. I operate with a first so. <n|a'a|n> <n|a' √n | √(n-1)> = n ???? Can someone please help me with the complete solution?