Hello, I have a question with the solution of the homework 4, exercise 3 :
How is this rotation matrix, represents a rotation of angle alpha around the x-axis ?
Shouldn't it be a rotation of alpha/2 ???
because in part b) we find :
And what we learned in linear algebra was that the rotation matrix looks like this :
so why is it a rotation of alpha and not alpha/2 ?
Kind Regards,
Thösam
Hi, good question,
Because its a rotation on the Bloch sphere and not a rotation in the plane. Qubit states are not vectors in the plane. Your final matrix (cos phi sin phi etc ... ) is the rotation matrix of angle phi in the plane. On the Bloch sphere there is this factor 1/2 which comes from the way we parametrize states. Therefore the matrix with alpha/2 is indeed a rotation of angle alpha on the Bloch sphere for quantum qubit states.
I hope this clarifies
Nicolas Macris
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