Quantum · undergrad

Quantum Angular Momentum

The operator algebra that controls orbital and spin angular momentum.

Published Apr 26, 2026 · 1 min

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Algebra

Angular momentum operators satisfy

[J_i,J_j]=i\hbar\epsilon_{ijk}J_k.

The simultaneous eigenstates of $J^2$ and $J_z$ obey

J^2|jm\rangle=\hbar^2j(j+1)|jm\rangle, \qquad J_z|jm\rangle=\hbar m|jm\rangle.

The noncommutativity measure that organizes quantum observables.

The master equation governing the time evolution of the wavefunction.

The simplest intrinsically quantum angular momentum system.