diff --git a/lecture_notes/1-27/Expectation Value Time Dependence b/lecture_notes/1-27/Expectation Value Time Dependence
index 874a1a1..4064fcd 100644
--- a/lecture_notes/1-27/Expectation Value Time Dependence	
+++ b/lecture_notes/1-27/Expectation Value Time Dependence	
@@ -14,3 +14,16 @@ Computed Derivative d/dt <Â>:
 	ħ                               dt 
 
 
+Computed Derivative (pic) d/dt <Â> (pic)
+
+Discovered/Introduced Commutator
+Cpmpatible Observables occur when commutator is equal to 0.
+
+[Ĥ,Â] = ĤÂ - ÂĤ
+
+Constant of Motion
+------------------
+    if d/dt Â = 0 and [Ĥ,Â] = 0,
+    then Â is a constant of motion
+
+    Thm: Two operators such that [Â,B̂] always have common Eigenstates