Electronic structure of a spherical quantum dot: Effects of the Kratzer potential, hydrogenic impurity, external electric and magnetic fields

Dehyar, A.; Rezaei, G.; Zamani, Ali

doi:10.1016/j.physe.2016.05.038

Cited by 31 publications

(10 citation statements)

References 29 publications

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“…For example, it was presented in the study of anharmonic oscillatory systems having potential energy of Kratzer type [23,24]. Relativistic and non-relativistic treatment of Hulthen-Kratzer potential and the Kratzer potential plus a dipole in 2D systems was discussed in [25][26][27]. The solution of two-dimensional Schrödinger equation for the Kratzer potential for low vibrational and rotational energy levels without and with a constant magnetic field having arbitrary Larmor frequencies have been studied in [28].…”

Section: Introductionmentioning

confidence: 99%

“…Effects of a Landau-type system on a neutral particle subjected to the Kratzer potential in a rotating frame was studied by Oliveira and Bakke [34]. In quantum mechanics, the VM is one way of finding approximations to the lowest energy eigenstate or ground state, and some excited states, but the AIM is applied to obtain highly accurate eigenvalues of the Schrödinger equation for several potential' energy systems [6,21,22,27,[35][36][37][38][39][40][41][42][43][44]. Singular inverse square potential in coordinate space with a minimal length was studied, regularised and renormalised with a generalised uncertainty principle, characterised by the existence of a minimal length [45][46][47].…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Etingof’s conjecture for quantized quiver varieties

Bezrukavnikov

Losev

2020

Invent. math.

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We propose the Whittaker function approach as a theoretical method for finding exact solutions of a quantum mechanical system placed in the Kratzer potential. We then show that the effect of an external uniform magnetic field on this system can be satisfactorily determined using variational method. By following the onestep treatment suggested in this study, we increase the reliability and the accuracy of the solutions of Schrödinger equation for a quantum mechanical system placed in potential energy and perturbed by a uniform magnetic field that proves to be useful in modelling physical phenomena. We find that the achieved numerical and analytical results agree very well with those already published and those calculated using the Numerov method.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Etingof’s conjecture for quantized quiver varieties

Bezrukavnikov

Losev

2020

Invent. math.

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“…[ 2 ] The ring‐shaped Kratzer potential has been used to determine the noncentral ro‐vibrational energies and wave functions. In this article, we introduce the scalar potential as a sum of the Kratzer potential [ 1–40 ] and a θ ‐dependent potential V 1 ( θ ) in the form

V ((),, r, θ) = D_{e} {(\frac{r - r_{e}}{r})}^{2} + \frac{V_{1} ((), θ)}{r^{2}}

where D e , r , and r e are respectively the dissociation energy, the internuclear distance, and the equilibrium intermolecular separation between two diatomic molecules, and the Aharonov‐Bohm (AB) flux field [ 41–50 ] as a vector potential takes the form

boldA = \frac{ℱ}{2 italicπr \sin θ} {\overset{falsê}{e}}_{ϕ},

where ℱ is the flux created within a very thin and infinitely long solenoid along the z direction. [ 41,42 ]

ℱ_{0} = \frac{ch}{e}

is called the flux quantum number, such that

\frac{ℱ}{{normalℱ}_{0}} \in normalℤ

.…”

Section: Introductionmentioning

confidence: 99%

“…[ 6,9 ] In the field of quantum chemistry, we have found many papers of radial Kratzer [ 3,7,8,19,25,26,28,32–39 ] and single or double ring‐shaped Kratzer [ 11–17,27 ] potential in three dimensions [ 4,20,22–24,40 ] and multidimensions. [ 5,18,21,29–31 ] The exact solutions and spectrum analysis of the radial Schrödinger equation for Kratzer potential have been carried out a few years ago in the absence of the AB field. [ 3,7,8,19,25,26,28,32–35,40 ] The Kratzer potential has two asymptotes at r = 0, ∞.…”

Section: Introductionmentioning

confidence: 99%

Localization effect on Rényi complexity of Kratzer potential in the presence of Aharonov‐Bohm field

Ghosh¹,

Nath

2020

Int J of Quantum Chemistry

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Exact wave functions are obtained for noncentral Kratzer potential in the presence of Aharonov‐Bohm flux field in terms of associate Laguerre and Jacobi polynomials. The exact form of Rényi entropy and generalized Rényi complexity are determined for positive integral order and , respectively. The narrowest confined and widest spread radial wave functions dominate the localization property of rotational wave functions for the optimum measure of Rényi entropy. The minimum and the maximum values of the Rényi entropy are found for the narrowest confined and widest spread radial wave functions, respectively. Conversely, the narrowest confined and widest spread rotational wave functions dominate the localization property of radial wave functions for the optimum measure of the generalized Rényi and shape Rényi complexities. If the generalized Rényi and shape Rényi complexities are minimum for the narrowest confined rotational wave function, then they will be maximum for the widest spread rotational wave function and vice versa.

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“…In a recent paper, we have shown results of the energy of the W-M exciton in spherical QD in Kratzer potential and its dependence on the size of QD, potential parameter, and permittivity of the medium [38]. So far, electronic properties have been studied mostly using this potential [37]. However, in this work, we extend our study to excitonic transitions, as in low dimensional systems, excitons play an imperative role in understanding the basic physics of the system.…”

Section: Introductionmentioning

confidence: 99%

Hydrogenic impurity effect on optical properties of Wannier-Mott exciton confined in a spherical quantum dot with Kratzer potential under magnetic field

Varsha

Giri²,

Arora³

et al. 2022

Rev. Mex. Fís.

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Confinement effects of Kratzer potential on a Wannier-Mott Exciton(W-M) are studied in a spherical quantum dot(QD) in the presence of a static magnetic field. Time independent Schr$\ddot{o}$dinger equation is solved numerically to obtain the energy states. The excitonic transitions so realized have been used to explore the non-linear optical properties that are important for optical characterization of materials such as the optical absorption coefficients (ACs) and refractive index changes (RICs). Impact of magnetic field, strength of the laser field and transition parameters using familiar compact density matrix approach are also analyzed. It has been observed that optical properties get radically modified under confinement effects. Also, the shift of degeneracy of different excitonic energy levels with the magnetic field in confinement potential has been reported for the first time for W-M exciton in the spherical quantum dot, the study that may have crucial input to the literature and myriad of practical implications.

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Electronic structure of a spherical quantum dot: Effects of the Kratzer potential, hydrogenic impurity, external electric and magnetic fields

Cited by 31 publications

References 29 publications

Etingof’s conjecture for quantized quiver varieties

Etingof’s conjecture for quantized quiver varieties

Localization effect on Rényi complexity of Kratzer potential in the presence of Aharonov‐Bohm field

Hydrogenic impurity effect on optical properties of Wannier-Mott exciton confined in a spherical quantum dot with Kratzer potential under magnetic field

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