A new deformed Schiöberg-type potential and ro-vibrational energies for some diatomic molecules

Mustafa, Omar

doi:10.1088/0031-8949/90/6/065002

Cited by 35 publications

(35 citation statements)

References 34 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In order to compare our findings with already published results, let us define the parameters D 0 = C 1 ,

D_{1} = C_{2} e^{- {br}_{e}},

D_{2} = C_{3} e^{- {br}_{e}}

, and

γ = \frac{ℏ^{2} normalℓ ((), normalℓ + 1)}{2 {mr}_{e}^{2}}

, to rewrite the energy spectrum as

E^{Sch} = {\overset{false˜}{P}}_{1} - - \frac{ℏ^{2} b^{2}}{2 m} {[\frac{2 n + 1 + h (q)}{4} - \frac{\frac{2 m}{b^{2} {normalℏ}^{2} Q^{2}} ({\overset{P}{true}}_{3} + Q {\overset{P}{true}}_{2}))}{2 n + 1 + h (q)}]}^{2}

where

frakturh ((), q) = \sqrt{1 + \frac{8 m}{ℏ^{2} b^{2}} {\overset{false˜}{P}}_{3} .}

which agrees with results obtained by Mustafa after identifying his parameters

{\overset{false˜}{P}}_{1} = P_{1} + γ C_{1}, {\overset{false˜}{P}}_{2} = P_{1} + γ C_{2},

{\overset{false˜}{P}}_{3} = P_{3} + γ C_{3}

.…”

Section: Some Useful Applicationssupporting

confidence: 87%

“…To deal with this potential we select the exponential parameters as follows:

A ((), q) = P_{2} e^{- {br}_{e}} q^{- 1}, B ((), q) = 0,

C ((), q) = P_{3} e^{- 2 {br}_{e}} q^{- 2}

, and

k = \frac{1}{b}

such that the potential in Equation becomes

V ((), r) = \frac{((), P_{2} e^{- {br}_{e}} q^{- 1}) {qe}^{- b false(r - r_{e false)}}}{1 - {qe}^{- b false(r - r_{e false)}}} + \frac{((), P_{3} e^{- 2 {br}_{e}} q^{- 2}) q^{2} e^{- 2 b false(r - r_{e false)}}}{{((), 1 - {qe}^{- b false(r - r_{e false)}})}^{2}}

from which, after using

Q = - {qe}^{{italicbr}_{e}}

, the new q ‐deformed Schiö berg‐type potential becomes

V^{Sch} ((), r) = P_{1} + V ((), r) = P_{1} + \frac{P_{2}}{e^{- italicbr} + Q} + \frac{P_{3}}{{((), e^{- italicbr} + Q)}^{2}} .

…”

Section: Some Useful Applicationsmentioning

confidence: 99%

See 1 more Smart Citation

Approximate ℓ‐bound state solutions of q‐deformed exponential‐type potentials

Peña

García-Ravelo

Ovando

et al. 2020

Int J of Quantum Chemistry

View full text Add to dashboard Cite

In this work, the exactly solvable Schrödinger equation for s-states of a class of multiparameter exponential-type potential (E-tP) is used to obtain the approximate ℓ 6 ¼ 0 bound state solutions for the corresponding q-deformed radial potentials. To deal with the effective potential, the Pekeris approximation for the centrifugal term is applied. The proposal has the advantage that, depending on the choice of the parameters involved in the E-tP, several q-deformed exponential potentials are obtained here as particular cases. That is, our proposition indicates that it is not necessary to use specialized methods to solve the Schrödinger equation for specific q-deformed exponential potentials. At this regard, in order to show the usefulness of the proposed method, we consider the ℓ 6 ¼ 0 bound state solutions of the q-deformed Tietz, Hulthén, Manning-Rosen, Shioberg, quadratic exponential, Wei and Hua among other potential models. Furthermore, with the example of the Hua potential we are contributing to solve the recent controversy on the energy spectra of this q-deformed model. Moreover, in some applications considered in this work the results can be used to correct similar findings already published. Besides, the proposal is useful when considering new q-deformed potentials with hypergeometric wavefunctions to be used in quantum chemical applications of diatomic molecules. K E Y W O R D Sℓ 6 ¼ 0 bound-state solutions, exponential-type models, Pekeris approximation, q-deformed potentials, Schrödinger equation

show abstract

“…In order to compare our findings with already published results, let us define the parameters D 0 = C 1 ,

D_{1} = C_{2} e^{- {br}_{e}},

D_{2} = C_{3} e^{- {br}_{e}}

, and

γ = \frac{ℏ^{2} normalℓ ((), normalℓ + 1)}{2 {mr}_{e}^{2}}

, to rewrite the energy spectrum as

E^{Sch} = {\overset{false˜}{P}}_{1} - - \frac{ℏ^{2} b^{2}}{2 m} {[\frac{2 n + 1 + h (q)}{4} - \frac{\frac{2 m}{b^{2} {normalℏ}^{2} Q^{2}} ({\overset{P}{true}}_{3} + Q {\overset{P}{true}}_{2}))}{2 n + 1 + h (q)}]}^{2}

where

frakturh ((), q) = \sqrt{1 + \frac{8 m}{ℏ^{2} b^{2}} {\overset{false˜}{P}}_{3} .}

which agrees with results obtained by Mustafa after identifying his parameters

{\overset{false˜}{P}}_{1} = P_{1} + γ C_{1}, {\overset{false˜}{P}}_{2} = P_{1} + γ C_{2},

{\overset{false˜}{P}}_{3} = P_{3} + γ C_{3}

.…”

Section: Some Useful Applicationssupporting

confidence: 87%

“…To deal with this potential we select the exponential parameters as follows:

A ((), q) = P_{2} e^{- {br}_{e}} q^{- 1}, B ((), q) = 0,

C ((), q) = P_{3} e^{- 2 {br}_{e}} q^{- 2}

, and

k = \frac{1}{b}

such that the potential in Equation becomes

V ((), r) = \frac{((), P_{2} e^{- {br}_{e}} q^{- 1}) {qe}^{- b false(r - r_{e false)}}}{1 - {qe}^{- b false(r - r_{e false)}}} + \frac{((), P_{3} e^{- 2 {br}_{e}} q^{- 2}) q^{2} e^{- 2 b false(r - r_{e false)}}}{{((), 1 - {qe}^{- b false(r - r_{e false)}})}^{2}}

from which, after using

Q = - {qe}^{{italicbr}_{e}}

, the new q ‐deformed Schiö berg‐type potential becomes

V^{Sch} ((), r) = P_{1} + V ((), r) = P_{1} + \frac{P_{2}}{e^{- italicbr} + Q} + \frac{P_{3}}{{((), e^{- italicbr} + Q)}^{2}} .

…”

Section: Some Useful Applicationsmentioning

confidence: 99%

Approximate ℓ‐bound state solutions of q‐deformed exponential‐type potentials

Peña

García-Ravelo

Ovando

et al. 2020

Int J of Quantum Chemistry

View full text Add to dashboard Cite

show abstract

“…We can cite the Nikiforov-Uvarov method [6], the function analysis [7], the asymptotic iteration [8], and the Feynman path integrals [24,25,26]. In recent papers, some q-deformed empirical potentials have been addressed, such as Woods-Saxon [20], the four-parametric deformed Schiöberg type [21,22] and the q-deformed hyperbolic Poschl-Teller potential [23].…”

Section: Introductionmentioning

confidence: 99%

“…Recently, Mustafa introduced a four-parametric deformed Schiöberg-type potential for diatomic molecules [21]. He computed the energy spectrum of the −states using the supersymmetric quantization in the Schrödinger framework.…”

Section: Introductionmentioning

confidence: 99%

Path integral treatment of the deformed Schiöberg-type potential for some diatomic molecules

2017

View full text Add to dashboard Cite

The bound state solution of the Feynman propagator with the deformed generalized Schiöberg potential is determined using an approximation of the centrifugal term. The energy eigenvalue expression is computed using Duru–Kleinert space–time transformation for both positive and negative deformation parameters of diatomic molecules. Besides, the rotation–vibration energy eigenvalues are numerically calculated for some diatomic molecules and compared with those given in the literature. The obtained results are in agreement with those given by state-of-the-art approximate and numerical methods.

show abstract

“…Just of recent, a modified form of Deng-Fan potential called the shifted Deng-Fan potential was suggested by Hamzavi et al (2013), it was reported that the shifted Deng Mustafa (2015) to investigate a new deformed Schioberg-type potential, and obtained ro-vibrational energies for some diatomic molecule [13]. He showed how this potential is related to the Deng-Fan potential [14]. Thus, the study of reflection and transmission coefficients of the symmetric barrier-type shifted Deng-Fan potential model is very necessary.…”

Section: Introductionmentioning

confidence: 99%

Reflection and Transmission Coefficients of the Symmetric Barrier-Type Shifted Deng–Fan Potential

Oluwadare¹,

Oyewumi²,

Thylwe³

et al. 2017

Commun. Theor. Phys.

View full text Add to dashboard Cite

By applying continuity and boundary conditions, the reflection and transmission coefficients of one-dimensional time-independent Schrödinger equation with a symmetric IntroductionThe scattering phenomena, such as scattering phase shifts, reflection and transmission coefficients are used to explain the behaviour of waves incident on a barrier [1-2]. The transmission coefficient represents the probability flux of the transmitted wave relative to that of the incident wave. It is often used to describe the probability of a particle tunneling through a barrier. This is more feasible in the case where electrons tunnel between two conducting materials. The shifted Deng-Fan potential is a suitable model for the theoretical predictions because it has been used extensively in both relativistic and non -relativistic quantum mechanics. The original Deng-Fan molecular potential has the correct asymptotic behaviour at the origin [3][4][5][6][7][8][9], and so, it has been used to predict the interactions between atoms and molecules and vibrational spectrum [3][4][5][6][7][8][9].

show abstract

A new deformed Schiöberg-type potential and ro-vibrational energies for some diatomic molecules

Cited by 35 publications

References 34 publications

Approximate ℓ‐bound state solutions of q‐deformed exponential‐type potentials

Approximate ℓ‐bound state solutions of q‐deformed exponential‐type potentials

Path integral treatment of the deformed Schiöberg-type potential for some diatomic molecules

Reflection and Transmission Coefficients of the Symmetric Barrier-Type Shifted Deng–Fan Potential

Contact Info

Product

Resources

About