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When acting on an eigenket, the phase factor <math>e^{(\alpha\beta^*-\alpha^*\beta)/2}</math> appears in each term of the resulting state, which makes it physically irrelevant.<ref>Christopher Gerry and Peter Knight: ''Introductory Quantum Optics''. Cambridge (England): Cambridge UP, 2005.</ref>
It
:<math>\hat{D}(\alpha)\hat{D}(\beta)=e^{\alpha\beta^*-\alpha^*\beta} \hat{D}(\beta)\hat{D}(\alpha)</math>
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