1Change of Basis Vectors Does Not Signify Compute Q in terms
of the helicity states 
and 
, showing that Q agrees with
Q computed from the energy eigenstates 
and 
.
2Change of Basis Vectors and the Trace Demonstrate the
conditions under which a change in the basis vectors of a system does not
change the trace Tr(M) 
of a matrix defined in that
system.
2Check of Eq. 11.13 Confirm by direct calculation that the self and distinct terms of eq. 11.13 behave as I claimed.
3Non-Commutativity Consider the issue of the non-commutativity of 
and 
by treating a concrete example: take a quantum system, find a
variable A which does not commute with 
, and compute 
and 
.