Displacement operator: Difference between revisions

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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 thean [[eigenstateseigenstate]] of the annihilation (lowering) operator.

== Properties ==