Computed Derivative d/dt :
d = d 〈Ψ(t)|Â|Ψ(t)〉
dt dt
⎛d 〈Ψ(t)⎞ Â|Ψ(t)〉 + 〈Ψ(t)|Â ⎛d Ψ(t)〉⎞ + 〈Ψ(t)|d Â|Ψ(t)〉
⎝dt ⎠ ⎝dt ⎠ dt
↓
ι 〈Ψ(t)|Ĥ Â|Ψ(t)〉 + 〈Ψ(t)|Â Ĥ -ι|Ψ(t)〉 + 〈Ψ(t)|d Â|Ψ(t)〉
ħ ħ dt
↓
ι 〈Ψ(t)|Ĥ Â - Â Ĥ|Ψ(t)〉 + 〈Ψ(t)|d Â|Ψ(t)〉
ħ dt
Computed Derivative (pic) d/dt (pic)
Discovered/Introduced Commutator
Cpmpatible Observables occur when commutator is equal to 0.
[Ĥ,Â] = ĤÂ - ÂĤ
Constant of Motion
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if d/dt  = 0 and [Ĥ,Â] = 0,
then  is a constant of motion
Thm: Two operators such that [Â,B̂] always have common Eigenstates