Recent content by kaltsoplyn

Strange, you should get the square root and I don't see anything wrong in my eqs. Besides your results should check against: [S_i,S_j]=i \hbar\epsilon_{i,j,k} S_k

Synthesizing high order spins starting from spin-1/2's is hard, although the procedure is straightforward. The formulas I give are general that's why they look so complex. However, it's not very hard to produce any such matrix if you plug these formulas in a symbolic mathematical software...

The equations I have posted solve your problem for any spin, integer or half-integer. Anyway, for spin = 1: S_x = \left( \begin{array}{ccc} 0 & \frac{1}{\sqrt{2}} & 0 \\ \frac{1}{\sqrt{2}} & 0 & \frac{1}{\sqrt{2}} \\ 0 & \frac{1}{\sqrt{2}} & 0 \end{array} \right) S_y =...

By using the spinor representation. In essence you are using combinations of spin-1/2 to represent the behaviour of arbitrarily large spins. This way you can generate operators and wavefunctions of large spins starting from the known spin-1/2 matrices. This was shown originaly by Majorana in...

This is an old thread, but people are bound to come back looking for these answers, so here's my 2 cents. For a given S, S_z comes from demanding S_z|S,m> = m |S,m> and is thus a diagonal (2S+1)x(2S+1) matrix with elements S, S-1,...,-S (Note: I assume |S,S> = (1,0,...,0) and |S,-S> =...