New formulation of nonlinear vector coherent states off-deformed spin–orbit Hamiltonians

Abstract

We provide, with a new formulation of vector, coherent states for nonlinear spin-orbit Hamiltonian models in terms of the matrix eigenvalue problem for generalized annihilation operators. Nonlinear quaternion vector coherent states are also discussed.

Oscillators in the Framework of Unified (q, α, β, γ, ν)-Deformation and Their Oscillator Algebras

“…6. The deformed C λ -extended oscillator algebra [21] is defined by the relations (8) where ν k ∈ R and H(K), K(N ) are real analytic functions. This algebra involves the two Casimir operators C 1 = e 2πN and C 2 = λ−1 k=0 e −2πi(N −k)/λ P k .…”

“…The q-deformed oscillators are used widely in the molecular and nuclear spectroscopies. A considerable attention was paid to nonlinear vector coherent states (NVCSs) of f -deformed spin-orbit Hamiltonians [8]. This class includes a multiparameter generalization of the one-and two-parameter deformed oscillator algebras [8][9][10][11][12][13][14].…”

“…A considerable attention was paid to nonlinear vector coherent states (NVCSs) of f -deformed spin-orbit Hamiltonians [8]. This class includes a multiparameter generalization of the one-and two-parameter deformed oscillator algebras [8][9][10][11][12][13][14]. Some of them have found applications to the investigation of various physical systems.…”

Unified (p, q; α, β, ν; γ) −deformed oscillator algebra: Irreducible representations and induced deformed harmonic oscillator

“…From the other side, there are some hopes that the deformed oscillator can be more suitable for physical studies of nonlinear phenomena than the usual bosonic oscillator of the standard quantum mechanics. Such hopes are supported by several applications in conformal field theory [2], in nuclear spectroscopy [3,4], in nonlinear quantum optics, in condensed matter physics [5], and in the description of systems with non-standard statistics and energy spectrum [6].…”

Nonclassical Properties of Even and Odd Semi-Coherent States

“…Also, significant progress was achieved in the development of practical realizable schemes of nonlinear quantum states, such as f-CS or nonlinear CS [9][10][11][12][13][14][15], even and odd CS [8,16] and semi CS [17]. These states have attracted much attention in recent decades due to their helpful applications in various fields of research [10,[18][19][20][21][22].…”