I am struggling to understand spin transformations and have used Sakurai's method of
|new basis> = U |old basis> to change basis vectors and hence should have
Sz' = Udagger Sz U
to transform the operator. I thought this should give Sz' = Sy in the workings (see attachment) but it gives Sx instead. If I use
Sz' = U Sz Udagger then I do get Sz'=Sy but according to the texts I have, the first arrangement is the correct form. So I'm really confused. Can anyone see what I'm doing wrong here.
I would be really grateful for any help with this. Thank you