Diagonal harmonious state representations
Let \(\{| u\rangle, n\in\mathbb{N}\}\) be the canonical basis in \(\ell^ 2(\mathbb{N})\). For \(z\) in the unit disk of the complex plane, define the ``harmonious state'': \(| z)=\sum_{n\geq 0} z^ n| n\rangle\). Formal representations of operators on \(\ell^ 2(\mathbb{N})\) in terms of the overcomplete set \(| z)\), analogous to the familiar coherent state representations, are written down.
scientific article; zbMATH DE number 465567