Thanks for the help.
Itai, that looks like exactly what I wanted. However, I still seem to get an error when I run the code you suggested
In[22]:= \[Rho][t_] := {{a[t], b[t]}, {c[t], d[t]}}
H[t_] := PauliMatrix[1]
DSolve[{I \[HBar] \[Rho]'[t] ==
H[t].\[Rho] - \[Rho].H[t], \[Rho][0] == PauliMatrix[3]}, {a, b, c,
d}, t]
During evaluation of In[22]:= DSolve::nolist: List encountered within {{{I \[HBar] (a^\[Prime])[t],I \[HBar] (b^\[Prime])[t]},{I \[HBar] (c^\[Prime])[t],I \[HBar] (d^\[Prime])[t]}}==-\[Rho].{{0,1},{1,0}}+{{0,1},{1,0}}.\[Rho]}. There should be no lists on either side of the equations. >>
Out[24]= DSolve[{{{I \[HBar] Derivative[1][a],
I \[HBar] Derivative[1][b]}, {I \[HBar] Derivative[1][c],
I \[HBar] Derivative[1][d][
t]}} == -\[Rho].{{0, 1}, {1, 0}} + {{0, 1}, {1,
0}}.\[Rho], {{a[0], b[0]}, {c[0], d[0]}} == {{1,
0}, {0, -1}}}, {a, b, c, d}, t][/b]
Do you know what this means?
