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Orbital angular momentum

{title2=$L_\pm$}

The operators $L_\pm=L_x\pm iL_y$ satisfy
$$
[L_z,L_\pm]=\pm\hbar L_\pm,
\qquad
[L^2,L_\pm]=0.
$$
They therefore change the <magnetic quantum number> $m$ by $\pm1$ while preserving the total angular-momentum quantum number $\ell$.

Angular momentum ladder operator

Past exam of the mathematics course of the University of Cambridge / 2021 / ib / Paper 4 / 15C / a / Solution

Angular momentum ladder operator ( $L_{\pm}$ )

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Angular momentum ladder operator (L±​)

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Angular momentum ladder operator ( $L_{\pm}$ )

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