Spin ladder operator ( $S_{\pm}$ )

The operators

S_{\pm} = S_{x} \pm i S_{y}

satisfy

S_{\pm} ∣ s, m ⟩ = ℏ s (s + 1) - m (m \pm 1) ∣ s, m \pm 1 ⟩ .

Table of contents
- Spin raising operator Spin ladder operator
- Spin lowering operator Spin ladder operator

Spin raising operator ( $S_{+}$ )

The spin raising operator

S_{+} = S_{x} + i S_{y}

increases the magnetic quantum number by one and annihilates the maximal-weight state.

Spin lowering operator ( $S_{-}$ )

The spin lowering operator

S_{-} = S_{x} - i S_{y}

decreases the magnetic quantum number by one and annihilates the minimal-weight state.

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