Spin Matrices - MATLAB Cody - MATLAB Central

Problem 2316. Spin Matrices

Difficulty:
(606)
Rate
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.
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!
Solve

Solution Stats

30.91% Correct | 69.09% Incorrect
Last Solution submitted on Nov 18, 2024

Problem Comments

Solution Comments

Show comments

Problem Recent Solvers9

Suggested Problems

More from this Author18

Problem Tags

physics spin

Community Treasure Hunt

Find the treasures in MATLAB Central and discover how the community can help you!

Start Hunting!
Go to top of page