Problem 2316. Spin Matrices

The spin of a particle is a fundamental property in quantum physics. We shall inspect below matrix representations of such spin operators.
Suppose you have integer or half-integer spin of value s. The matrices Sx, Sy and Sz representing it have the following properties:
  • Si (with i={x,y,z}) are traceless Hermitian matrices;
  • Commutation relations (a): [ Si,Sj ] = i εijk Sk, where [·,·] is the commutator and εijk is the Levi-Civita symbol.
  • Commutation relations (b): [ Si,S² ] = 0, where = Sx²+Sy²+Sz²;
  • Eigenvalues: = j(j+1)·I and Sz = diag( -j/2, -j/2+1, … ,j/2-1, j ), where I is the identity matrix.
See also this article for more reference.
Examples
[Sx,Sy,Sz] = spin_matrices(1/2)
Sx =
0 0.5
0.5 0
Sy =
0 -0.5i
0.5i 0
Sz =
0.5 0
0 -0.5
Note:
The usual cheats are not allowed!

Solution Stats

20.45% Correct | 79.55% Incorrect
Last Solution submitted on May 25, 2023

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