Rotation operator (quantum mechanics)

This article concerns the rotation operator, as it appears in quantum mechanics. == Quantum mechanical rotations == With every physical rotation R {\displaystyle R} , we postulate a quantum mechanical rotation operator D ^ ( R ) : H → H {\displaystyle {\widehat {D}}(R):H\to H} that is the rule that assigns to each vector in the space H {\displaystyle H} the vector | α ⟩ R = D ^ ( R ) | α ⟩ {\displaystyle |\alpha \rangle _{R}={\widehat {D}}(R)|\alpha \rangle } that is also in H {\displaystyle H} .

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