Factorization method for exact solution of the non-central modified Killingbeck potential plus a ring-shaped-like potential

Mbadjoun, B. Tchana; Ema’a, J. M. Ema’a; Yomi, J; Abiama, P. Ele; Ben-Bolie, G. H.; Ateba, P. Owono

doi:10.1142/s021773231950072x

“…Such potentials are employed in the study of non-spherically symmetric problems that often occur in chemistry. A number of articles have been devoted to the study of non-central potentials [22][23][24][25][26][27][28][29][30][31][32][33][34][35][36][37].…”

Section: Introductionmentioning

confidence: 99%

Particle confined in modified ring-shaped potential

Talwar

¹

,

Lumb

²

,

Sen

³

et al. 2020

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The spectrum of a particle confined in Hulthén plus ring-shaped potential is obtained by solving the time-independent Schrödinger equation numerically. The effect of potential parameters on various properties of the particle have been investigated in detail. The energy levels, radial matrix elements, oscillator strengths and polarizabilities of the particle have been found to show strong dependence on the confining potential parameters. The presence of the ring potential is found to appreciably alter the angular part of dipole matrix elements. Also, it is shown that the comparison theorem of Quantum Mechanics for energy eigenvalues for four different potentials, viz., Coulomb, Hulthén, Yukawa and Hulthén2 is independent of the presence of ring potential.

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“…The probability current density and the corresponding current for this dressed state has been calculated using equations ( 11) and ( 13), respectively. The corresponding timedependent induced magnetic field has been calculated using equations (21) and (22). The charge currents due to RCPL pulse are localized in the x-y plane whereas the generated magnetic field lies along the z-axis.…”

Section: Theorymentioning

confidence: 99%

“…Motivated by the work of by Yuan et al [4] and as an extension to the earlier work [18,19], the present work has been carried out for the study of a hydrogen atom confined in Hulthén plus ringshaped potential perturbed by a femtosecond right circularly polarized laser (RCPL) pulse. The ring potential employed in the present case belongs to the class of non-central potentials [20,21]. Such potentials depending on radial as well as angular part of the system are important since the representative potentials for realistic physical systems may often deviate from the conventional spherical models like Coulomb or Yukawa potentials.…”

Section: Introductionmentioning

confidence: 99%

Generation of charge currents and magnetic pulses

Lumb

¹

,

Talwar

²

,

Prasad

³

2020

J. Phys. B: At. Mol. Opt. Phys.

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The generation of charge currents and hence induced magnetic field in a spherically bound hydrogen atom by an ultrafast right circularly polarized laser pulse has been studied. The atom is assumed to be under the effect of a Hulthén plus a ring-shaped potential. The simultaneous effect of pulse parameters such as El0, tp and ω0, the cavity radius, r0, and parameters related to the non-central potential has been investigated. These parameters have been found to significantly affect the magnitude of generated current as well as the magnetic field and thus play an important role in determining the response of the system to external laser. The laser pulse is found to produce femtosecond magnetic pulses. Such magnetic pulses have many biomedical applications. Hulthén screening or ring deformation potential reduces the magnitude of current and induced magnetic field for an unbounded atom. On the other hand, for the bounded case, the potential parameters are found to have a positive impact on these quantities.

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“…Similarly, the application of Hellmann-Feynman Theorem provides a less mathematical approach of obtaining expectation values of a quantum mechanical systems [27,28]. Some of the potential models considered within the framework of relativistic and nonrelativistic wave equations are Hulthen-Yukawa Inversely quadratic potential [29], noncentral Inversely quadratic potential [30], Modified Hylleraas potential [31], Yukawa, Hulthen, Eckart, Deng-Fan, Pseudoharmonic, Kratzer, Woods-Saxon, double ring shape, Coulomb, Tietz-Wei, Tietz-Hua, Deng-Fan, Manning-Rosen, trigonometric Rosen-Morse, hyperbolic scalar, and vector potential and exponential type potentials among others [32][33][34][35][36][37][38][39][40][41][42][43][44][45][46][47][48][49][50]. Coulomb, hyperbolic, and screened exponential type potentials have been of interest to researchers in recent times because of their enormous applications in both chemical and physical sciences.…”

Section: Introductionmentioning

confidence: 99%

Approximate Solutions, Thermal Properties, and Superstatistics Solutions to Schrödinger Equation

Okon

¹

,

Onate

²

,

Omugbe

³

et al. 2022

Advances in High Energy Physics

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In this work, we apply the parametric Nikiforov-Uvarov method to obtain eigensolutions and total normalized wave function of Schrödinger equation expressed in terms of Jacobi polynomial using Coulomb plus Screened Exponential Hyperbolic Potential (CPSEHP), where we obtained the probability density plots for the proposed potential for various orbital angular quantum number, as well as some special cases (Hellmann and Yukawa potential). The proposed potential is best suitable for smaller values of the screening parameter α . The resulting energy eigenvalue is presented in a close form and extended to study thermal properties and superstatistics expressed in terms of partition function Z and other thermodynamic properties such as vibrational mean energy U , vibrational specific heat capacity C , vibrational entropy S , and vibrational free energy F . Using the resulting energy equation and with the help of Matlab software, the numerical bound state solutions were obtained for various values of the screening parameter ( α ) as well as different expectation values via Hellmann-Feynman Theorem (HFT). The trend of the partition function and other thermodynamic properties obtained for both thermal properties and superstatistics were in excellent agreement with the existing literatures. Due to the analytical mathematical complexities, the superstatistics and thermal properties were evaluated using Mathematica 10.0 version software. The proposed potential model reduces to Hellmann potential, Yukawa potential, Screened Hyperbolic potential, and Coulomb potential as special cases.

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Factorization method for exact solution of the non-central modified Killingbeck potential plus a ring-shaped-like potential

Cited by 8 publications

References 20 publications

Particle confined in modified ring-shaped potential

Particle confined in modified ring-shaped potential

Generation of charge currents and magnetic pulses

Approximate Solutions, Thermal Properties, and Superstatistics Solutions to Schrödinger Equation

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