Generalized coherent states for associated hypergeometric-type functions

Generalized photon-added associated hypergeometric coherent states: characterization and relevant properties

“…The curves show that the measure has a singularity at x = |z| 2 = 0 and tends to zero for x → ∞. For p = 0, we recover, as expected, the measure ω 0 (|z| 2 ; m) = |c| 2 π obtained in our previous work [21] for the corresponding ordinary coherent states. .…”

“…respectively. We proved in [21] that the generalized coherent states (24) verify the properties of label continuity, overcompleteness, temporal stability and action identity.…”

“…The latters are eigenstates of the annihilation operator denoted a m . Following Aleixo et al [20], we introduced, in a previous paper [21], a right inverse operator a −1 m allowing the definition of generalized associated hypergeometric CS (GAH-CS). In this paper, we present the construction of a new family of CS, hereafter called generalized photon-added associated hypergeometric CS (GPAH-CS), obtained by adding photons to the conventional associated hypergeometric CS.…”

Pöschl-Teller Hamiltonian: Gazeau-Klauder type coherent states, related statistics, and geometry

“…The knowledge of the quantum metric enables to calculate quantum mechanical transition probability and uncertainties. [41][42][43] The map z  −→ |z, γ⟩ ν defines a map from the space C of complex numbers onto a continuous subset of unit vectors in Hilbert space and generates in the latter a two-dimensional surface with the following Fubini-Study metric:…”

Shape Invariant Potential Formalism for Photon-Added Coherent State Construction

“…These states were first introduced by Schrödinger [34] since 1926 for the harmonic oscillator. Then followed decades of intensive works in order to extend the CS concept to other types of exactly solvable systems [5,6,17,20,28]. It was shown in 1980's that a large class of these solvable potentials are characterized by a single property, i.e., a discrete reparametrization invariance, called shape-invariance [11,14,16,23], introduced in the framework of the supersymmetric quantum mechanics (SUSY QM) [10,21].…”