- #1

siddharth5129

- 94

- 3

S[itex]^{2}[/itex]{sm} = h[itex]^{2}[/itex]s(s+1){sm} ; S[itex]_{z}[/itex]{sm} = hm{sm} to

S+-{sm} = h(s(s+1) - m(m+1))[itex]^{1/2}[/itex]{s(m+-1)}

( I couldn't find the appropriate mathematical notation in the menus, but the {} is a 'ket' , h is actually h/2[itex]\pi[/itex] and the +- should be a + on top of the - ) where S+- = S[itex]_{x}[/itex] +- iS[itex]_{y}[/itex]

I don't get what he did here at all. And finally, he claims this - "But this time eigenvectors are not spherical harmonics ( not functions of phi and theta at all), and there is no "a priori" reason to exclude half-integer values of s and m."

Why is the eigenvector not being a spherical harmonic a reason at all to include the half-integer values of s and m?

Sorry for the long post, but this has been causing me considerable distress. I'd be so eternally grateful for some help figuring this out :)