2nd quantization of angular momentum

Given a system with Angular Momentum Operators $J_{i}, i \in {1, 2, 3}$ , we define the Ladder operators as $J_{\pm} = J_{1} \pm i J_{2}$ . This definition satisfies

$[J^{2}, J_{\pm}] = 0$ , where $J^{2} := \sum_{i = 1}^{3} J_{i}^{2}$
$J_{\pm} J_{\mp} = J^{2} - J_{3}^{2} \pm ℏ J_{3}$
$[J_{+}, J_{-}] = 2ℏ J_{3}$
$[J_{3}, J_{\pm}] = \pm ℏ J_{\pm}$

🌊 CollapsedWave

Explorer

2nd quantization of angular momentum

Backlinks

Graph View