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The quantum numbers $+\frac{1}{2}$ and $-\frac{1}{2}$ for the electron spin represent
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two quantum mechanical spin states which have no classical analogues
The quantum numbers $+\frac{1}{2}$ and $-\frac{1}{2}$ indicate the rotation of electrons around its axis in opposite directions. Hence, they represent the two quantum mechanical spin states which have no classical analogues.
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