Dynamics of SU(1,1) coherent states for the time-dependent quadratic Hamiltonian system

Exact solutions of the Schrödinger equation for the pseudoharmonic potential: an application to some diatomic molecules

“…Gur and Mann [30] have used the SU (1, 1) SGA method to construct the associated radial Barut-Girardello coherent states for the isotropic harmonic oscillator in arbitrary dimension and these states have been mapped into the Sturm-Coulomb radial coherent states. The dynamics of the SU (1, 1) coherent states for the time-dependent quadratic Hamiltonian system has been discussed by Choi [36].…”

“…Apart from generating the eigenvalues and eigenfunctions, this approach offers the additional advantages in that it can be used to find the matrix elements in a simple way, and it is also very useful in constructing coherent states of a given Hamiltonian system [30,36,38]. Thus, Gur and Mann [30] used SGA approach to construct the radial Barut-Girardello coherent states for the isotropic harmonic oscillator in arbitrary dimension and mapped these states into Sturm-Coulomb radial coherent state; the dynamics of SU(1, 1) coherent states are investigated for the time-dependent quadratic Hamiltonian system by Choi [36].…”

“…Thus, Gur and Mann [30] used SGA approach to construct the radial Barut-Girardello coherent states for the isotropic harmonic oscillator in arbitrary dimension and mapped these states into Sturm-Coulomb radial coherent state; the dynamics of SU(1, 1) coherent states are investigated for the time-dependent quadratic Hamiltonian system by Choi [36]. Very recently, the second lowest and second highest bases of the discrete positive and negative irreducible representations of SU (1, 1) Lie algebra via spherical harmonics are used to construct generalized coherent states by Dehghani and Fakhri [38].…”

Information theories for time-dependent harmonic oscillator

“…Among many interesting features of HUR for different potentials, it is noticeable that HUR for the systems bound by homogeneous power potentials is independent of the coupling strength scaling of the potentials [2] while in some cases it oscillates with time [3]. A fundamental feature of quantum mechanics is that measurement brings about uncontrollable disturbance on the measured object.…”

SU(1,1) Coherent States for the Generalized Two-Mode Time-Dependent Quadratic Hamiltonian System

“…The former may be generated by means of a process including the competition between nondegenerate parametric amplification and nondegenerate two-photon absorption, while the generation of the latter can be attained from the unitary evolution of two-mode number states driven by a nondegenerated parametric device [20]. It is noticed that SU(1, 1) coherent states reveal the nonclassical properties such as squeezing effect, nontrivial zero-point energy, violations of the Cauchy-Schwarz inequality, and fluctuation of uncertainty products [21,22]. Since the SU(1, 1) coherent states for one-mode TDQHS have been already studied [6], the investigation of the SU(1, 1) coherent states in the present work will be focused on the generalized two-mode TDQHS through the formulation of SU(1, 1) Lie algebra.…”