I'm trying to implement the solution described in 12.4.1 Measurements on a Single Spin of this book:
sJ = (\[HBar]/2) PauliMatrix /@ {1, 2, 3};
normal = {Sin[\[Theta]] Cos[\[Phi]], Sin[\[Theta]] Sin[\[Phi]],
Cos[\[Theta]]};
sigmaN = normal . PauliMatrix /@ {1, 2, 3};
Eigensystem[sigmaN] // FullSimplify // Transpose // MatrixForm
Then I try to check the Hermitian property of the sigmaN matrix as follows, but all failed:
HermitianMatrixQ[sigmaN]
FullSimplify[
sigmaN, { \[Theta], \[Phi] } \[Element] Reals] // HermitianMatrixQ
For more details, please refer to the attachment.
Regards, HZ
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