Thermodynamic properties and approximate solutions of the ℓ-state Pöschl–Teller-type potential

In this study, we obtained the position-momentum uncertainties and some uncertainty relations for the Pöschl-Teller-type potential for any ℓ. The radial expectation values of r −2 , r 2 and p 2 are obtained from which the Heisenberg Uncertainty principle holds for the potential model under consideration. The Fisher information is then obtained and it is observed that the Fisher-information-based uncertainty relation and the Cramer-Rao inequality hold for this even power potential. Some numerical and graphical results are displayed.

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“…Also, n = 0, 1, 2, ..., [λ], where [λ] denotes the largest integer inferior to λ. The wave function is obtained as [24] R nℓ = s…”

Section: Position-momentum Uncertainty Relationsmentioning

confidence: 99%

Quantum information entropies for the $$\ell $$ ℓ -state Pöschl–Teller-type potential

2016

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“…However, it is important to understand that obtaining the wave function for a particular quantum system requires solving a relativistic or nonrelativistic wave equation (Eyube et al, 2019b;Eyube et al, 2019c). The Schrödinger wave equation is fundamental and is particularly useful in the description of spinless particles (Yahya and Oyewumi, 2016;Eyube et al, 2019b). For a given potential energy model, the solution of Schrödinger equation is dependent on the presence of the centrifugal term in the effective potential of the equation (Yanar et al, 2020;Eyube et al, 2020a).…”

Section: Introductionmentioning

confidence: 99%

Energy Spectrum and Some Useful Expectation Values of the Tietz-Hulthén Potential

Bitrus¹,

Wadata²,

Nwabueze³

et al. 2021

FJS

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In this paper, concept of supersymmetric quantum mechanics has been employed to derive expression for bound state energy eigenvalues of the Tietz-Hulthén potential, the corresponding equation for normalized radial eigenfunctions were deduced by ansatz solution technique. In dealing with the centrifugal term of the effective potential of the Schrödinger equation, a Pekeris-like approximation recipe is considered. By means of the expression for bound state energy eigenvalues and radial eigenfunctions, equations for expectation values of inverse separation-squared and kinetic energy of the Tietz-Hulthén potential were obtained from the Hellmann-Feynman theorem. Numerical values of bound state energy eigenvalues and expectation values of inverse separation-squared and kinetic energy the Tietz-Hulthén potential were computed at arbitrary principal and angular momentum quantum numbers. Results obtained for computed energy eigenvalues of Tietz-Hulthén potential corresponding to Z = 0 and V0 = 0 are in excellent agreement with available literature data for Tietz and Hulthén potentials respectively. Studies have also revealed that increase in parameter Z results in monotonic increase in the mean kinetic energy of the system. The results obtained in this work may find suitable applications in areas of physics such as: atomic physics, chemical physics, nuclear physics and solid state physics

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“…The solution of the Schrodinger equation (SE), Klein Gordon (KGE) and Dirac equations (DE) have been attracted the attention of many researchers in theoretical physics area (Durmus and Yasuk, 2007;Karayer, 2019;Yahya and Oyewumi, 2016) because these equations contain all information on the quantum mechanics system. The SE is used to analyze the quantities of nonrelativistic systems, while the KGE and DE are used in relativistic systems to analyze the spin-0 and spin-1 2 particles, respectively (Arda and Sever, 2009;Candemir, 2016;Zarrinkamar et al, 2010).…”

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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Thermodynamic properties and approximate solutions of the ℓ-state Pöschl–Teller-type potential

Cited by 25 publications

References 21 publications

Quantum information entropies for the $$\ell $$ ℓ -state Pöschl–Teller-type potential

Quantum information entropies for the $$\ell $$ ℓ -state Pöschl–Teller-type potential

Energy Spectrum and Some Useful Expectation Values of the Tietz-Hulthén Potential

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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