Effects of cosmic-string framework on the thermodynamical properties of anharmonic oscillator using the ordinary statistics and the q-deformed superstatistics approaches

Sobhani, Hadi; Hassanabadi, H.; Chung, Won Sang

doi:10.1140/epjc/s10052-018-5581-y

Cited by 34 publications

(11 citation statements)

References 32 publications

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“…Our results show that the expression for the energy in Ref. [1] is wrong, probably due to erroneous calculations in the manipulation of the biconfluent Heun equation. The correct quantization condition is obtained applying two conditions: the condition (17) is used to obtain constraints between the potential parameters and the condition (18) is used to obtain the expression of energy eigenvalues.…”

mentioning

confidence: 65%

“…It is worthwhile to mention that all results depend mainly on the energy spectrum of the system. The purpose of this comment is point to out a misleading treatment on the solution of the biconfluent Heun equation, this fact jeopardizes the results of [1].…”

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confidence: 96%

“…al. [1] have studied the thermodynamical properties of the anharmonic oscillator within cosmic-string framework using ordinary statistic and the q-deformed superstatistics approaches. To achieve their goal, the authors need to calculate the wave function and the energy spectrum, which have been obtained from the Schrödinger equation within a cosmic-string framework mapped into biconfluent Heun differential equation.…”

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confidence: 99%

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Comment on “Effects of cosmic-string framework on the thermodynamical properties of anharmonic oscillator using the ordinary statistics and the q-deformed superstatistics approaches”

Neto

Castro

2018

Eur. Phys. J. C

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We point out a misleading treatment in a recent paper published in this Journal (Sobhani et al., Eur Phys J C 78:106, 2018) regarding solutions for the Schrödinger equation with a anharmonic oscillator potential embedded in the background of a cosmic string mapped into biconfluent Heun equation. This fact jeopardizes the thermodynamical properties calculated in this system.In a recent paper in this Journal, Sobhami et. al. [1] have studied the thermodynamical properties of the anharmonic oscillator within cosmic-string framework using ordinary statistic and the q-deformed superstatistics approaches. To achieve their goal, the authors need to calculate the wave function and the energy spectrum, which have been obtained from the Schrödinger equation within a cosmic-string framework mapped into biconfluent Heun differential equation. It is worthwhile to mention that all results depend mainly on the energy spectrum of the system. The purpose of this comment is point to out a misleading treatment on the solution of the biconfluent Heun equation, this fact jeopardizes the results of [1].The time-independent Schrödinger equation with an anharmonic oscillator potential embedded in the background of a cosmic string is given byRedefining the wave function as Φ(ρ) = R(ρ) √ ρ , one can remove the first derivative and rewrite Eq.(1) as a

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confidence: 65%

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confidence: 96%

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confidence: 99%

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Comment on “Effects of cosmic-string framework on the thermodynamical properties of anharmonic oscillator using the ordinary statistics and the q-deformed superstatistics approaches”

Neto

Castro

2018

Eur. Phys. J. C

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“…Soon after this seminal report, it turned out that Tsallis statistics is very useful in the analyses of overall nonextensive dynamical phenomena, including black-body radiation 5 , gravitation 6 , Euler turbulence 7 , biological evolution 8 , intrinsic inhomogeneities in manganites 9 , nonlinear dynamical dissipation 10 , etc. 11 , 12 .…”

Section: Introductionmentioning

confidence: 99%

Analysis of the effects of nonextensivity for a generalized dissipative system in the SU(1,1) coherent states

Choi

2022

Sci Rep

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The characteristics of nonextensivity for a general quantum dissipative oscillatory system in the SU(1,1) coherent states are investigated using the invariant operator method. We consider a deformed Caldirola-Kanai oscillator represented in terms of a parameter q which is a measure of the degree of nonextensivity. The nonextensivity effects on the parametric evolution of the SU(1,1) coherent states are elucidated. We compare our results with those of previous researches and address the advantage of our methodology which adopts the linear invariant operator. In particular, the nonextensive behaviors associated with the fluctuations of canonical variables and the dissipation of quantum energy are analyzed in detail regarding their dependence on q. The properties of SU(1,1) coherent states that we adopt here can be utilized in quantum-information processes such as cloning, swapping, and teleportation of state information.

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“…Some of them are the thermodynamical properties for systems with double ring-shaped quantum dot type potential (Khordad and Sedehi, 2018), thermodynamical properties from Klein Gordon equation with DFPEP potential D-dimensional spaces (A N . For example, thermodynamical properties from Schrodinger Equation and Klein Gordon equation with Poshcl-Teller potential (Yahya and Oyewumi, 2016), thermodynamical properties of Schrodinger equation with an anharmonic oscillator in cosmic string framework (Sobhani, et al, 2018), thermodynamical properties of diatomic molecules using general molecular potential (A N Ikot et al, 2018).…”

Section: Introductionmentioning

confidence: 99%

Analysis of Energy and Wave Functions and the Thermodynamics Properties of the 6-Dimensional Schrodinger Equation Under Double Ring-Shape Oscillator (Drso) and Manning-Rosen Potentials Using Susy Qm Method

Bilaut¹,

Супармі²,

Cari³

et al. 2020

PTQ

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The exact solutions of the Schrodinger equations (SE) in the D-dimensional coordinate system have attracted the attention of many theoretical researchers in branches of quantum physics and quantum chemistry. The energy eigenvalues and the wave function are the solutions of the Schrodinger equation that implicitly represents the behavior of a quantum mechanical system. This study aimed to obtain the eigenvalues, wave functions, and thermodynamic properties of the 6-Dimensional Schrodinger equation under Double Ring-Shaped Oscillator (DRSO) and Manning-Rosen potential. The variable separation method was applied to reduce the one 6-Dimensional Schrodinger equation depending on radial and angular non-central potential into five onedimensional Schrodinger equations: one radial and five angular Schrodinger equations. Each of these onedimensional Schrodinger equations was solved using the SUSY QM method to obtain one eigenvalue and one wave function of the radial part, five eigenvalues, and five angular wave functions angular part. Some thermodynamic properties such, the vibrational mean energy 𝑈, vibrational specific heat 𝐶, vibrational free energy 𝐹, and vibrational entropy 𝑆, were obtained using the radial energy equations. The results showed that except the 𝑛𝑙1, all increment of angular quantum number decreases the energy values. Increments of all potential parameter increase the energy values. Increment of angular quantum number and potentials parameter increases the amplitude and shifts the wave functions to the left. However, the increment of 𝑛𝑙1, 𝛼, 𝜎, and 𝜌 decrease the amplitude and shift wavefunctions to the right. Moreover, the vibrational mean energy 𝑈 and free energy 𝐹 increased as the increasing value of potentials parameters, where the ω parameter has the dominant effect than the other parameters. The vibrational specific heat 𝐶 and entropy 𝑆 affected only by the 𝜔 parameter, where 𝐶 and 𝑆 decreased as the increase of 𝜔.

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Effects of cosmic-string framework on the thermodynamical properties of anharmonic oscillator using the ordinary statistics and the q-deformed superstatistics approaches

Cited by 34 publications

References 32 publications

Comment on “Effects of cosmic-string framework on the thermodynamical properties of anharmonic oscillator using the ordinary statistics and the q-deformed superstatistics approaches”

Comment on “Effects of cosmic-string framework on the thermodynamical properties of anharmonic oscillator using the ordinary statistics and the q-deformed superstatistics approaches”

Analysis of the effects of nonextensivity for a generalized dissipative system in the SU(1,1) coherent states

Analysis of Energy and Wave Functions and the Thermodynamics Properties of the 6-Dimensional Schrodinger Equation Under Double Ring-Shape Oscillator (Drso) and Manning-Rosen Potentials Using Susy Qm Method

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