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 S² = Sx²+Sy²+Sz²;
- Eigenvalues: S² = j(j+1)·I and Sz = diag( -j/2, -j/2+1, … ,j/2-1, j ), where I is the identity matrix.
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
Problem Comments
-
2 Comments
Jean-Marie Sainthillier
on 17 May 2014
Not a problem for me...
Georges
on 9 Sep 2014
Neither for me :D
Solution Comments
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