(q; l, λ)-Deformed Heisenberg Algebra: Coherent States, Their Statistics and Geometry

The Heisenberg algebra is deformed with the set of parameters {q, l,λ} to generate a new family of generalized coherent states respecting the Klauder criteria. In this framework, the matrix elements of relevant operators are exactly computed. Then, a proof on the sub-Poissonian character of the statistics of the main deformed states is provided. This property is used to determine the induced generalized metric.