O|o>=o|o>

<oj|oi>= (0 | i!=j; 1 i==j)

|a> = sum(a_o |o>)

<a| = sum(<o|a_o*)

<O> = <a|O|a>/<a|a>=<a|Oa>/<a|a>=(sum(|a_o|^2*o)/sum(|a_z|^2))

O=e^(-iHt)