No hand soving at all Please only do them as MATLABWOLFRAMs

No hand soving at all! Please only do them as MATLAB/WOLFRAM\'s MATHMATICA CODE/SCRIPT. NO SELF CALCULATIONS

MATLAB/WOLFRAM\'s MATHMATICA CODE/SCRIPT ONLY

MATLAB/WOLFRAM\'s MATHMATICA CODE/SCRIPT ONLY PLEASE

Solution

Ans C: U† = exp(iH†) = [H is Hermitian] = exp(iH)
U†U = exp(iH) exp(iH) = [H commutes with itself] =
= exp(iH + iH) = exp(0) = 1
Since U†U = 1, U is unitary.

printf(\"which is comparable to machine precision eps = %e.\ \ \",\\
eps);
tioA =
4 -3 -1
-2 3 -1
-2 -3 5
tioB =
8 -3 1
-2 9 -1
2 -3 7
tioC =
2 5 0
5 8 2
0 2 0
A and B commute: [A, B] =
0 0 0
0 0 0
0 0 0
C does not commute with A: [A, C] =
-0.050000 -0.150000 0.010000
0.110000 0.090000 0.090000
-0.150000 -0.300000 -0.040000
... nor does it commute with B: [B, C] =
-0.050000 -0.210000 -0.030000
0.130000 0.090000 0.070000
-0.070000 -0.180000 -0.040000
exp(A) * exp(B) =
3.730627729180000 -2.113764332011219 0.205255403221727
-1.409176221340812 3.935883132401728 -0.704588110670406
0.410510806443453 -2.113764332011218 3.525372325958274
and exp(A+B) =
3.730627729180001 -2.113764332011218 0.205255403221727
-1.409176221340812 3.935883132401727 -0.704588110670406
8