Spin Quantum Number

$\backslash Vert\; \backslash mathbf\{s\}\; \backslash Vert\; =\; \backslash sqrt\{s\; \backslash ,\; (s+1)\}\; \backslash ,\; \backslash hbar$

$\backslash mathbf\{s\}$ is the quantized spin vector,

$\backslash Vert\; \backslash mathbf\{s\}\backslash Vert$ is the norm of the spin vector,

$s$ is the spin quantum number associated with the spin angular momentum

$s\_z\; =\; m\_s\; \backslash ,\; \backslash hbar$

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