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The name of this operator is derived from its ability to displace a localized state in phase space by a magnitude <math>\alpha</math>. It may also act on the vacuum state by displacing it into a [[coherent state]]. Specifically,
<math>\hat{D}(\alpha)|0\rangle=|\alpha\rangle</math> where <math>|\alpha\rangle</math> is a [[coherent state]], which is an [[eigenstate]] of the annihilation (lowering) operator. This operator was introduced independently by [[Richard Feynman]] and [[Roy J. Glauber]] in 1951.<ref>{{Cite journal |last=Dodonov |first=V. V. |date=2002 |title='Nonclassical' states in quantum optics: a 'squeezed' review of the first 75 years |url=https://iopscience.iop.org/article/10.1088/1464-4266/4/1/201 |journal=Journal of Optics B: Quantum and Semiclassical Optics |volume=4 |issue=1}}</ref>
== Properties ==
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