Representations of coherent states in non-orthogonal bases

2003/10/23 by S. Twareque Ali, S Twareque Ali, R. Roknizadeh +3 · 3 citations
Mathematics · Physics and Astronomy · #Mathematical Analysis and Transform Methods #Nonlinear Waves and Solitons #Quantum Mechanics and Non-Hermitian Physics #math-ph #math.MP #physics.atom-ph #quant-ph

paper · pdf · doi:10.1088/0305-4470/37/15/009

arxiv created 2003/10/23 · openalex publication_date 2004/03/29 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/30

Abstract

Starting with the canonical coherent states, we demonstrate that all the so-called nonlinear coherent states, used in the physical literature, as well as large classes of other generalized coherent states, can be obtained by changes of bases in the underlying Hilbert space. This observation leads to an interesting duality between pairs of generalized coherent states, bringing into play a Gelfand triple of (rigged) Hilbert spaces. Moreover, it is shown that in each dual pair of families of nonlinear coherent states, at least one family is related to a (generally) non-unitary projective representation of the Weyl–Heisenberg group, which can then be thought of as characterizing the dual pair.

Citations

• Nonclassical properties of states generated by the excitations on a coherent state

Cited by

• Pseudobosons, Riesz bases, and coherent states
• Superpositions of the dual family of nonlinear coherent states and their non-classical properties
• Construction of the dual family of Gazeau–Klauder coherent states via temporally stable nonlinear coherent states