How is equation 4.61 derived from n dot s in the Arbitrary Spin Operator?

[nateHI]

http://www.tampa.phys.ucl.ac.uk/~tania/QM4226/SEC4B.pdf

At the above link, I'm not quite sure how the instructor got to the matrix definition for Sn(equation 4.61 on page 4) from n dot s. Does someone know of a link that doesn't skip that step?

 

[Petr Mugver]

At the above link, I'm not quite sure how the instructor got to the matrix definition for Sn(equation 4.61 on page 4) from n dot s. Does someone know of a link that doesn't skip that step?

Well, n = (sin(theta) cos(phi), sin(theta) sin(phi), cos(theta)) is the radial versor, and the Pauli matrices (sigmax, sigmay, sigmaz) are the usual ones... take the scalar product... what don't you understand exactly?

 

[t_barlow]

I'm not sure what the lower case s is, I think it should be upper case, i.e. the operator defined in eqn 4.52. The components of S are the pauli matrices times hbar/2 as in 4.55.

 

[nateHI]

OK I get it. It was a silly mistake. I was getting table 4.60 mixed up with the pauli matrices. Thanks.