HMW4 exercise 3.c Pauli Y

HMW4 exercise 3.c Pauli Y

par David Loïck Claude Lacour,
Nombre de réponses : 2

Hello,

Sorry, I'm stuck at the exercise with the exponential with a  Pauli matrice Y:

I don't know how to prove that is is a rotation around the Y axis. I don't know if I can use trigonometric identities to go further or to multiply by a phase to get a form that I can represent on the Bloch Sphere. Could some one help me please? 

Thank you for your answers 


En réponse à David Loïck Claude Lacour

Re: HMW4 exercise 3.c Pauli Y

par Victor Braun,
A rotation around the y-axis or x-axis is pretty "unnatural" for the spherical coordinates, as both phi and theta change. So finding a formula for a general case is very cumbersome, that is why we always use easy cases. However, to prove it in a general way, one could take both components in exponential form and then phase out the ket so that the first component is real (and then a cosine).