Displacement operator: Difference between revisions

Revision as of 08:44, 24 July 2010

Revision as of 18:20, 27 October 2010

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which shows us that:

<math>\hat{D}(\alpha)\hat{D}(\beta)= e^{(\beta\alpha\beta^*-\alpha\beta^*\beta)/2} \hat{D}(\alpha + \beta)</math>

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>