Alireza Dehghani

Alireza Dehghani
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  • Professor
  • Faculty Member at Payame Noor University

In search of peace

About

91
Publications
11,526
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746
Citations
Introduction
Alireza Dehghani (AD) has a degree in physics with honors (2004) from the University of Tabriz, where he obtained his Ph.D. in Theoretical Physics (2009) with the thesis Symmetries & Coherent states in Quantum mechanics. He is currently a researcher and professor(full) of Physics at the University of PayameNoor. AD and coworkers have been significantly contributing to putting the attention of the scientific community on the topic of Para-Bose states in quantum systems.
Current institution
Payame Noor University
Current position
  • Faculty Member
Additional affiliations
January 2015 - February 2016
Payame Noor University
Position
  • Professor (Associate)
August 2009 - November 2015
Payame Noor University
Position
  • vice-chancellor
Position
  • quantum mechanics and mathematical physics
Education
August 2003 - July 2005
university of tabriz
Field of study

Publications

Publications (91)
Article
Following the lines of the recent papers (Ann. Phys. 362, 659670 (2015) and Mod. Phys. Lett. A 37, 1550198 (2015)), we introduce even and odd \(\lambda\)-deformed binomial states (\(\lambda\)-deformed BSs) \( \vert M,\eta,\lambda\rangle_{\pm}\), in which for \(\lambda =0\), they lead to ordinary even and odd binomial states (BSs). We show that thes...
Article
Full-text available
A theoretical scheme is proposed to generate a strongly entangled photon pair by a \(\Lambda \)-configured three-level atom interacting with a two-mode quantized cavity field through two strong classical fields resonating with the corresponding atomic transitions. The initial state of the two-mode cavity field is considered to be the tensor product...
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The scheme of an arrangement is considered for the preparation of some non-classical superposed states from squeezed states by using the optical parametric amplifier (OPA) apparatus, which is based on an idea recently proposed to generate photon-added states from the coherent states of light. This technique allows one to obtain linear combinations...
Article
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Here we apply a two-mode Binomial-like superposition of the photon-number operators (GSP operation) on each mode of the entangled coherent-squeezed states (ECSS), which are called GSP-ECSS from here on. In order to gain more insight into the effectiveness of this operation, and for comparison with the case already discussed as the photon-added ECSS...
Article
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Based on the f-oscillator formalism, we introduce a nonlinear optomechanical framework that is constructed from the standard optomechanical system by deforming the single-mode photonic-field operators. Such a generalized optomechanical system describes an intensity-dependent interaction of a mechanical oscillator with a single-mode electromagnetic...
Article
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This paper demonstrates a new formalism of producing some entangled states attached to a two-particle system. We explain how these entangled states come directly from a new algebraic method through the cross-product of two spin coherent states. They lead to various quantum states with considerable nonclassical properties, and are capable candidates...
Article
We study the exact Markovian and non-Markovian dynamics of entanglement, excited-state population, and quantum memory-assisted entropic uncertainty of two dipole-dipole interacting atom qubits inside a leaky cavity. The qubits move inside the cavity and interact with a classical driving laser field. Besides analyzing the possibility of steady-state...
Article
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Based on the quantum memory-assisted entropic uncertainty relation (QMA-EUR), we investigate the Markovian and non-Markovian dynamics of entanglement witness in a two-atom system that asymmetrically are coupled to a leaky cavity with two-photon relaxation. The atoms are two-level systems, they move inside the cavity and interact with a classical dr...
Book
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Advanced quantum mechanics
Data
Outstanding Reviewer of Journal of physics B-2018
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We study quantum discord dynamic of two atomic qubits moving inside a leaky cavity, where the two-qubit system is driven by a classical field. We suppose that the qubits are coupled to each other through dipole-dipole interaction and interacting asymmetrically with the cavity field via a two-photon relaxation. Using the time-dependent Schrödinger e...
Article
We analyzed the exact Markovian and non-Markovian dynamics of two atoms, allowing for dipole–dipole and Ising-like interplays between them, coupled asymmetrically to a leaky cavity via two-photon relaxation. Beside analyzing the conditions to preserve the initial atoms entanglement trough relaxation into the steady state of the system, we establish...
Article
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In continuation of previous papers [Quantum Inf. Process doi 10.1007/s11128-015-1223-6 and Appl. Phys. B 123 (2017) 181], we proposed a new class of two-mode entangled nonlinear coherent-squeezed states (ENCSS) where the standard coherent states are substituted by nonlinear coherent states. Here we employ different types of non-linearity functions...
Article
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We introduce a unitary operator which may be constructed conveniently by exploiting the properties of the Glauber displacement and parity operators. We show that it can be considered as a constant of motion of a quantum system including pure dephasing interaction of a central qubit with a nano-mechanical resonator.Using the eigenvectors of the Glau...
Article
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In this study, we introduce a new class of two-mode qutrit-like entangled states based on the `Near' coherent states. They link to a specific class of non-classical states, namely, photon added coherent states, which makes them capable candidates in quantum information processes. Based on these states, various superpositions such as the two-qubit e...
Article
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We study a quantum heat engine (QHE) with a working medium described by a parity-deformed Jaynes-Cummings (JC) model consisting of two identical two-level atoms interacting with a single-mode para-Bose field in a cavity. Compared to the standard two-atom JC model, this model introduces the action of a specific local classical field as an external c...
Article
Full-text available
Two new configurations of superposition of quantum states corresponding to the angular momentum of spin-1 quantum system is proposed in this article. One is a trivial state, |β, α⊥〉≡ (I −|α〉〈α|)|β〉, which consists of two Klauder’s type of spin coherent state |α〉 and |β〉 that is also perpendicular to |α〉, and the other is a non-trivial case composed...
Book
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حالتهاي غيركلاسيكي ميدان تابشي در پژوهشهاي اخير در زمينه ي مكانيك كوانتومي و به ويژه در اپتيك كوانتومي از جايگاه خاصي برخوردار هستند. مفهوم حالت هاي همدوس ابتدا توسط شرودينگر در سال 1926 هنگام بررسي دسته اي از حالتهاي مكانيك كوانتومي كه رفتاري شبه كلاسيك دارند، مطرح گرديد
Book
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نظریه مکانیک کوانتومی امروزه به کامل ترین توصیف بشر در درك ساز و کارهاي عالم هستی به ویژه در ابعاد بنیادین تبدیل شده است. علی رغم سخت بودن درك مفاهیم این نظریه، انطباق بسیار جذاب آن با آزمایش و تجربه، سبب تعجب هر فرد مبتدي یا کارآزموده آشنا به قوانین فیزیک می شود . این دیدگاه در کنار مکانیک کلاسیک و الکترومغناطیس بنیان اندیشه و تفکر فیزیکدانان در ع...
Conference Paper
A quantum system consisting of two coupled two-level atoms interacting with two-mode quantized field in an optical cavity is studied as a working substance in a quantum Otto cycle, and it has been shown that the system of interest can act as a quantum heat engine. The effect of atom-field coupling strengths during the quantum adiabatic expansion an...
Article
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Nonlinear coherent states or f-coherent states are one of the important class of quantum states of light attached to the f-deformed oscillators. They have been introduced in a pioneering work by Manko et al. and have been realized physically as the stationary states of the centre of mass motion of a trapped ion by de Matos Filho et al. To gain insi...
Article
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We propose a scheme for dissipative preparation of maximal entanglement in a two-qubit Heisenberg XXZ model interacting asymmetrically with two independent boson thermal reservoirs with different temperature. One reservoir is common to both qubits, while the other is connected with just one qubit. We analytically and numerically investigate the ste...
Article
Full-text available
Recently, the dynamics simulation of light-harvesting complexes as an open quantum system, in the weak and strong coupling regimes, has received much attention. In this paper, we investigate a digital quantum simulation approach of the Fenna–Matthews–Olson (FMO) photosynthetic pigment-protein complex surrounded with a Markovian bath, i.e. memoryles...
Article
Full-text available
In line with an experimentally feasible protocol was proposed by A. Asadian et al. [ PRL 112, 190402 (2014)], we introduce a pure dephasing model where the interaction of the central qubit with a nano-mechanical resonator is affected by a spin-bath to study the dynamics of resonator-qubit entangled states. We show that how system-bath coupling as w...
Article
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The present work is devoted to studying the entanglement dynamics of two central spins coupled in a spin environment and subjected, simultaneously, to an external magnetic field changing with time t as an exponential function \({\mathfrak {B}}\left( 1-\mathrm{e}^{-\lambda t}\right) \). We want to determine whether interaction among central spins wi...
Article
Full-text available
We consider a parity-deformed Jaynes-Cummings model (JCM) consists of two identical two-level atoms interacting with a single-mode para-Bose field in a cavity. Compared to the standard JCM, this model introduces the action of a specific local classical field as an external control which can be simulated through an intensity-dependent two-atom JCM w...
Article
Full-text available
In continuation of previous papers where the addition of photons into the two-mode entangled quantum states was studied, we proposed a scheme to establish and generate photon-added ‘entangled Barut–Girardello coherent states’ (PAEBGCSs), by applying photon creation operators on the two-mode EBGCSs, where the latter is introduced by Hach et al. (JOS...
Preprint
Full-text available
In continuation of previous papers where the addition of photons into the two-mode entangled quantum states were studied, we proposed a scheme to establish and generate photon-added `entangled Barut-Girardello coherent states' (PAENBGCSs), by apply- ing photon creation operators on the two modes EBGCSs, where the latter is introduced by Hach III et...
Preprint
Full-text available
In this paper, we introduce a new kind of photon-added entangled coherent states (PA-ECSs), by performing repeatedly a f-deformed photon-addition (DPA) operation, A† = f(ˆn)a†, on each mode of the entangled coherent states (ECSs), |�±(�)�. By choosing a particular deformation function f(ˆn), we study how the entanglement properties can be enhanced...
Article
Full-text available
In this paper, we introduce a new kind of photon-added entangled coherent states (PA-ECSs), by performing repeatedly a f-deformed photon-addition (DPA) operatio, on each mode of the entangled coherent states (ECSs), |Ψ±(α). By choosing a particular deformation function f(ˆn), we study how the entanglement properties can be enhanced by DPA operatio...
Article
Full-text available
As in two previous papers where nonclassical properties and entanglement dynamics were studied for entangled nonlinear coherent states (ENCS) [D. Afshar and A. Anbaraki, J. Opt. Soc. Am. B 33, 558 (2016).] and for photon-added entangled nonlinear coherent states (PAENCS) [A. Anbaraki, D. Afshar and M. Jafarpour, Eur. Phys. J. Plus 133, 2 (2018).],...
Article
Full-text available
Othman and Yevick, [1] in 2018 introduced a new class of states de�ned as near coherent states attached to the simple harmonic oscillator. Such states can be expressed as superposition of a standard coherent state and a derivative state, which are neither completely quantum nor completely classical. Here, we introduce photon-added (-depleted) near...
Article
Full-text available
As in two previous papers where nonclassical properties and entanglement dynamics were studied for entangled nonlinear coherent states (ENCS) [D. Afshar and A. Anbaraki, J. Opt. Soc. Am. B 33, 558 (2016).] and for photon-added entangled nonlinear coherent states (PAENCS) [A. Anbaraki, D. Afshar and M. Jafarpour, Eur. Phys. J. Plus 133, 2 (2018).],...
Article
Full-text available
We investigate the effects of parity-deformed fields on the dynamics of entanglement transfer to distant noninteracting atomic qubits. These qubits are embedded in two distant lossy cavities connected by a leaky short-length fiber (or additional cavity). The process is studied within a single-excitation subspace, the parity-deformed cavity photons...
Article
Full-text available
Using the parity deformed Heisenberg algebra (RDHA), we first establish associated coherent states (RDCSs) for a pseudo-harmonic oscillator (PHO) system that are defined as eigenstates of a deformed annihilation operator. Such states can be expressed as superposition of an even and odd Wigner cat states.35 The RDCSs minimize a corresponding uncerta...
Article
Full-text available
In this paper, we introduce quasi-Bell states as a result of two-mode superposition of two “Near” coherent states, | α, δθ⟩ , shifted in phase by π and π2, where the latter introduced by Othman et al. as a new class of quantum states attached to the simple harmonic oscillator which generated via a Mach–Zehnder interferometer. To gain insight into u...
Article
Full-text available
In this paper, a Hamiltonian model that includes interaction of two coupled two-level atoms with a nondegenerate parametric amplifier in a cavity is introduced. By using the two-mode squeezing operator and under a certain condition, the introduced Hamiltonian is reduced to a generalized Jaynes–Cummings Hamiltonian. The constants of motion of system...
Article
Full-text available
Following the lines of the recent papers (Daneshmand and Tavassoly, Int. J. Theor. Phys. 56, 1218 (2017)), we study quantum mechanical treatments of an interaction between a two level atom with a single-mode field in the two-photon Jaynes-Cummings model, where the Hamiltonian of the field is considered to be the quantized Caldirola-Kanai (CK) Hamil...
Article
Full-text available
We introduce new configurations of (anti-)symmetric superpositions of two ‘near’-coherent states,|α, δθ), shifted in phase by π, the latter being introduced by Othman et al. as a new class of quantum states attached to the simple harmonic oscillator and also generated via a Mach–Zehnder interferometer. To gain an insight into the effectiveness of t...
Preprint
Full-text available
We investigate the dynamics of entanglement transfer to distant noninteracting atom qubits embedded in two separated lossy cavities which are connected by a leaky fiber. The process is realized through parity-deformed radiation fields acting on the subsystems to conveniently describe the interaction with continuous and static local classical fields...
Article
Full-text available
The construction of nonlinear coherent states via a unitary displacement operator is possible only for a few quantum-mechanical systems. In this paper, we define two non-unitary and a unitary displacement operators with the help of corresponding f-deformed bosonic annihilation and creation operators. While the action of the non-unitary displacement...
Article
Full-text available
In this paper, we consider a Hamiltonian model that includes interaction of two coupled two-level atoms with a single-mode quantized electromagnetic field in a cavity via the degenerate two-photon transition. The cavity is filled with a Kerr-like medium and is held at a temperature T. The free field Hamiltonian possesses the su(1,1) symmetry which...
Article
In this paper, we use a para-Bose operator to construct new kinds of excited para-Bose states. These states may be considered as appropriate and linear combinations of the para-Bose Fock states. We prove that these states satisfy a closure relation that is expressed uniquely in terms of the Meijer G -function. We examine the nonclassical properties...
Article
In this paper, we use a para-Bose operator to construct new kinds of excited para-Bose states. These states may be considered as appropriate and linear combinations of the para-Bose Fock states. We prove that these states satisfy a closure relation that is expressed uniquely in terms of the Meijer G-function. We examine the nonclassical properties...
Article
Full-text available
In this paper, we introduce two classes of superposed states generated by a superposition of two single-mode para-Bose coherent states (CS) with arbitrary relative phase factors. The first class is superposition of two opposite para-Bose CS and second class consists of two para-Bose CS, π 2 out of phase with each other. These states are reduced to...
Article
The problem of photon addition to the deformed coherent states (para-Bose states) [Phys. Rev. A. 95 043835 (2017)] and deformed cat states [Ann. Phys. 362, 659 (2015)] associated with the pseudo-harmonic oscillator are studied in this research. It is demonstrated that photon-added deformed coherent states are finite superpositions of a wide class o...
Article
Full-text available
We define generalized cat states as linear superpositions of the semi-coherent states. They can be considered as superpositions of two distinguishable components of the Schr¨odinger cat states. We study the statistical properties of the introduced states in detail. The physical properties of these states, like the sub-Poissonian statistics and norm...
Article
In this paper, we introduce photon-added and photon-subtracted “semi”-coherent field states. These states are constructed via the boson operator actions on the semi-coherent states (P.M. Mathews, K. Eswaran, Nuovo Cimento B 17, 332 (1973)). These are not a family of the f-deformed coherent states, however they can be considered as superpositions of...
Article
We proposed a scheme to generate new class of even(odd) compass stat es (specific superpositions of Wigner cat states [A. Dehghani et al., Ann. Phys. 362, 659 (2015)]), in the presence of the paritydeformed Jaynes–Cummings Hamiltonia n [A. Dehghani et al., Sci. Rep. 6, 38069 (2016)] describing acoupled system comprising a two-level atom and a cavity...
Article
Full-text available
The parity-deformations of the quantum harmonic oscillator are used to describe the generalized Jaynes-Cummings model based on the λ-analog of the Heisenberg algebra. The behavior is interestingly that of a coupled system comprising a two-level atom and a cavity field assisted by a continuous external classical field. The dynamical characters of th...
Preprint
A one-parameter generalized Wigner-Heisenberg algebra( WHA) is reviewed in detail. It is shown that WHA verifies the deformed commutation rule $[\hat{x}, \hat{p}_{\lambda}] = i(1 + 2\lambda \hat{R})$ and also highlights the dynamical symmetries of the pseudo-harmonic oscillator( PHO). \textbf{The present article is devoted to the study of new cat-s...
Preprint
A parity deformed Jaynes-Cummings model (JCM) is introduced, which describes an interaction of a two-level atom with a $\lambda$-deformed quantized field. In the rotating wave approximation (RWA), all eigen-values and eigen-functions of this model are obtained exactly. Assuming that initially the field is prepared in the Wigner cat state (WCS) and...
Article
A new family of semi coherent states (semi-CSs), for a charged particle moving in a constant uniform magnetic field have been introduced. We have shown that they can be interpreted as nonlinear coherent states (NLCSs) with a special nonlinearity function. By investigation on some of their nonclassical features, it has bee shown that contrary to the...
Article
Full-text available
By using Wigner–Heisenberg algebra (WHA) and its Fock representation, even and odd Wigner negative binomial states (WNBSs) |M,ξ,ν〉±W (ν = 0 corresponds to the ordinary even and odd negative binomial states (NBSs)) are introduced. These states can be reduced to the Wigner cat states in special limit. We establish the resolution of identity property...
Article
We study the quantum correlation dynamics of bipartite spin-\(\frac {1}{2}\) density matrices for two particles under Wigner rotations induced by Lorentz transformations which is transmitted through noisy channels. We compare quantum entanglement, geometric discord(GD), and quantum discord (QD) for bipartite relativistic spin-\(\frac {1}{2}\) state...
Article
Exact analytical solutions for the two-mode nondegenerate parametric amplifier have been obtained by using the transformation from the two-dimensional harmonic oscillator Hamiltonian. Some important physical properties such as quantum statistics and quadrature squeezing of the corresponding states are investigated. In addition, these states carry c...
Article
In this paper, we introduce even and odd deformed photon added nonlinear coherent states which in a special case lead to the even and odd photon-added coherent states |z, m〉±. After choosing a particular nonlinearity function corresponding to the Pöschl-Teller potential, we show that they satisfy the over-completeness relation and thus are coherent...
Article
Following systematic strategies, which were introduced by M. M. Nieto in 1995, coherent states (CSs) may be derived from their generating functions. In the present paper we generalize the latter procedure to new types of generating functions of even and odd Hermite polynomials. In this case, new CSs are obtained, as superposition of even and Fock s...
Article
Full-text available
We introduce excited coherent states, β , α ; n ≔ a † n β , α , where n is an integer and states β , α denote the coherent states of a charged particle in a uniform magnetic field. States β , α minimize the Schrödinger-Robertson uncertainty relation while having the nonclassical properties. It has been shown that the resolution of ide...
Article
Full-text available
A new configuration of superposition of quantum states is proposed in this article to produce the angular momentum coherent states, |α, β⟩ := |α⟩ × |β⟩. Which are composed of cross products of two different copies of spin coherent states, |α⟩ and |β⟩. It has been shown that the cross products of two coherent vectors remain coherent again. They repr...
Data
We introduce in this paper new kinds of coherent states for some quantum solvable models such as an electron moving in flat surface subject to perpendicular constant and decaying (Morse like) magnetic field. We explain how these states come directly from generating functions of certain families of classical orthogonal polynomials without the comple...
Article
Full-text available
Based on previous work [A. Dehghani, B. Mojaveri, J. Phys. A 45, 095304 (2012)], we introduce photon-subtracted generalised coherent states (PSGCSs) |z,m⟩ r : = a m |z⟩ r , where m is a nonnegative integer and |z⟩ r denote the generalised coherent states (GCSs). We have shown that the states |z,m⟩ r are eigenstates of a non-Hermitian operator f(n̂...
Article
Full-text available
In this paper, we construct a new class of generalized photon added coherent states (GPACSs), by excitations on a newly introduced family of generalized coherent states (GCSs) (A Dehghani and B Mojaveri 2012 J. Phys. A: Math. Theor. 45 095304), obtained via generalized hypergeometric type displacement operators acting on the vacuum state of the si...
Article
We introduce to this paper new kinds of coherent states for some quantum solvable models: a free particle on a sphere, one-dimensional Calogero-Sutherland model, the motion of spinless electrons subjected to a perpendicular magnetic field B, respectively, in two dimensional flat surface and an infinite flat band. We explain how these states come di...
Article
We introduce to this paper new kinds of coherent states for some quantum solvable models: a free particle on a sphere, one-dimensional Calogero-Sutherland model, the motion of spinless electrons subjected to a perpendicular magnetic field B, respectively, in two dimensional flat surface and an infinite flat band. We explain how these states come di...
Article
A new scheme is proposed to design excited coherent states. where the states ${\beta}$,${\alpha}$ denote the Glauber two variable minimum uncertainty coherent states, which minimize minimum uncertainty conditions while carrier nonclassical properties too and n is an integer. They are converted into the Agarwal's type of the photon added coherent st...
Article
In this paper we define a non-unitary displacement operator, which by acting on the vacuum state of the pseudo harmonic oscillator (PHO), generates new class of generalized coherent states (GCSs). An interesting feature of this approach is that, contrary to the Klauder-Perelomov and Barut-Girardello approaches, it does not require the existence of...
Preprint
Full-text available
In this paper we define a non-unitary displacement operator, which by acting on the vacuum state of the pseudo harmonic oscillator (PHO), generates new class of generalized coherent states (GCSs). An interesting feature of this approach is that, contrary to the Klauder-Perelomov and Barut-Girardello approaches, it does not require the existence of...
Article
The most general displaced number states, based on the bosonic and an irreducible representation of the Lie algebra symmetry of su(1, 1) and associated with the Calogero-Sutherland model are introduced. Here, we utilize the Barut-Girardello displacement operator instead of the Klauder-Perelomov counterpart, to construct new kind of the displaced nu...
Article
Following the lines of the recent papers [J. Phys. A 44, 495201 (2012); B. Mojaveri, A. Dehghani, Eur. Phys. J. D 67, 179 (2013)], we construct here a new class of generalized coherent states related to the Landau levels, which can be used as the finite Fock subspaces for the representation of the su(2) Lie algebra. We establish the relationship be...
Article
Full-text available
The most general displaced number 'coherent' states, based on the Heisenberg, su(2) and su(1, 1) Lie algebras symmetries, are constructed. They depend on two parameters, and can be converted into the well-known photon-added, two variable Glauber coherent states and displaced number states respectively, depending on which of the parameters is equal...
Article
The idea of construction of the nonlinear coherent states based on the hypergeometric- type operators associated to the Weyl-Heisenberg group [J:P hys:A 45(2012) 095304], are generalized to the similar states for the arbitrary Lie group SU(1; 1). By using of a discrete, unitary and irreducible representation of the Lie algebra su(1; 1) wide range o...
Article
The Glauber minimum-uncertainty coherent states with two variables for Landau levels, based on the representation of Weyl-Heisenberg algebra by two different modes, have been studied about four decades ago. Here, we introduce new twovariable coherent states with minimum uncertainty relationship for Landau levels in three different methods: the infi...
Article
The main goal of this paper is to present an alternative method to construct new kinds of nonlinear coherent states. To do this, we first establish a class of hypergeometric type of generalized displacement operators, 1Fr([0], [0, 1, …, r − 1], za†), act on the vacuum state of the harmonic oscillator and generate normalized quantum states of the Fo...
Article
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The purpose of this paper is to use the idea in J. Geom. Phys.42, 54 (2002) to compute the topological charges for a (finite) sequence of noncommutative line bundles over the fuzzy sphere. Central to this task is to construct projective modules associated with sequence of the irreducible sub-representations of the tensor product of two different ir...
Article
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We show that the non-Hermitian Hamiltonians of the simple harmonic oscillator with $\mathcal{PT}$ and $\mathcal{C}$ symmetries involve a pseudo generalization of the Heisenberg algebra via two pairs of creation and annihilation operators which are $\mathcal{T}$-pseudo-Hermiticity and $\mathcal{P}$-anti-pseudo-Hermiticity of each other. The non-unit...
Article
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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. Depending on whether the representation label is an even or odd integer, each of the new coherent states is separated into two different class...
Article
Full-text available
Barut–Girardello coherent states corresponding to the (l−m)- and (l+m)-integer discrete irreducible representations of su(1,1) Lie algebra are calculated by the spherical harmonics Ylm(θ,ϕ). Their explicit compact forms and also, to realize the resolution of the identity, their corresponding positive definite measures on the complex plane are obtai...
Article
Full-text available
Using second-order differential operators as a realization of the su(1,1) Lie algebra by the associated Laguerre functions, it is shown that the quantum states of the Calogero-Sutherland, half-oscillator and radial part of a 3D harmonic oscillator constitute the unitary representations for the same algebra. This su(1,1) Lie algebra symmetry leads t...
Article
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In Chenaghlou and Faizy (Int. J. Theor. Phys. 2008), the authors claim that they have constructed the Barut-Girardello coherent states for the parabolic cylinder functions. However, we point out here that by introducing these coherent states, Schrödinger was able to put forth the idea of “coherent states of the quantum harmonic oscillator” over eig...
Article
Full-text available
It is well known that the magnetic quantum number m of monopole harmonics describes quantization corresponding to the z-component of the angular momentum operator in the framework of su(2) symmetry algebra. Here, it is shown that the azimuthal quantum number l allocates itself a ladder symmetry by the operators which are described in terms of l. Fu...
Article
Full-text available
In a recently published paper in this journal [A. Cheaghlou and O. Faizy, J. Math. Phys. 49, 022104 (2008)], the authors introduce the Gazeau-Klauder coherent states for the trigonometric Rosen-Morse potential as an infinite superposition of the wavefunctions. It is shown that their proposed measure to realize the resolution of the identity conditi...
Article
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We call attention to the misconstructions in a paper recently published in this journal [A. Chenaghlou and O. Faizy, J. Math. Phys.48, 112106 (2007)]. It is shown that the constructed Barut–Girardello coherent states are problematic from the view points of the definition and the measure. The claimed coherencies for the Kravchuk functions cannot act...
Article
Full-text available
Using the ladder operators shifting the index m of the associated Jacobi functions, for a given n, the monopole harmonics and their corresponding angular momentum operators are, respectively, extracted as the irreducible representation space and generators of su(2) Lie algebra. The indices n and m play the role of principal and azimuthal quantum nu...

Questions

Questions (5)
Question
As we know the ‘sum’ of two angular momenta is an angular momentum in the tensor product space. In other word, for two Hermitian operators J, K acting on V1, V2 respectively, and satisfying SU(2) cummutation relation. the ‘sum’ of angular momenta,J+K, is an angular momentum in the tensor product, V1 ⊗ V2. where the commutators of the operators in the different spaces vanish i.e. [J,K]=0.
Is it possible to use addition theorem for two coupled angular momentum operators?
Question
do we have any application of vector(or cross) product of wave functions in quantum mechanics?
Question
in quantum mechanics solutions of Hamiltonian constitute orthogonal basis of Hilbert space which equiped with inner product
Question
As we know eigenfunctions of Hamiltonian (quantum states) constitute a Hilbert space (vector space) which equipped with an inner product.
Question
do we have any application of vector(or cross) product in quantum mechanics?

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