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Fixed formula of prod of disp operators. Added details |
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When acting on an eigenket, the phase factor <math>e^{(\beta\alpha^*-\alpha\beta^*)/2}</math> appears in each term of the resulting state, which makes it physically irrelevant.<ref>Gerry, Christopher, and Peter Knight: ''Introductory Quantum Optics''. Cambridge (England): Cambridge UP, 2005.</ref>
== Alternative expressions ==
Two alternative ways to express the displacement operator are:
:<math>\hat{D}(\alpha) = e^{ -\frac{1}{2} | \alpha |^2 } e^{+\alpha \hat{a}^{\dagger}} e^{-\alpha^{*} \hat{a} } </math>
:<math>\hat{D}(\alpha) = e^{ +\frac{1}{2} | \alpha |^2 } e^{-\alpha^{*} \hat{a} }e^{+\alpha \hat{a}^{\dagger}} </math>
== Multimode displacement ==
The displacement operator can also be generalized to multimode displacement.
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