Systematic search of exactly solvable ring-shaped potential using the transformation method

Bharali, Arup

doi:10.1088/0031-8949/88/03/035009

Cited by 8 publications

(4 citation statements)

References 42 publications

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“…Noting that the s-states exist for other non-central potentials (see for instance Refs. [5,7] and references therein), we deduce that the absence of these states in our case is not due to the difference between the symmetry of the s-states (which are central) and that of…”

Section: Discussionsupporting

confidence: 55%

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Schrödinger equation for non-pure dipole potential in 2D systems

Moumni

Falek

2016

Journal of Mathematical Physics

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In this work, we analytically study the Schrödinger equation for the (non-pure) dipolar ion potential V (r) = q/r + D cos θ/r 2 , in the case of 2D systems using the separation of variables and the Mathieu equations for the angular part. We give the expressions of eigenenergies and eigenfunctions and study their dependence on the dipole moment D. Imposing the condition of reality on the energies E n,m implies that the dipole moment must not exceed a maximum value otherwise the corresponding bound state disappears.We also find that the s states (m = 0) can no longer exist in the system as soon as the dipole term is present.

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Section: Discussionsupporting

confidence: 55%

“…Refs. [5][6][7] and references therein). However, as demonstrated by Hautot [3], only few of these potentials in fact have analytical solutions, and they have thus been dominantly considered with either numerical technics or approximation methods.…”

Section: Introductionmentioning

confidence: 99%

Schrödinger equation for non-pure dipole potential in 2D systems

Moumni

Falek

2016

Journal of Mathematical Physics

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“…The study of this kind of potential began with the works of Makarov [6] and Hartmann [7] in molecular systems and now they are in focus in various fields, especially in quantum chemistry and nuclear physics. For example they were used for the description of ring-shaped molecules like benzene and also for the interactions between deformed pair of nuclei [8][9][10][11]. Recently, many studies have been devoted to the study of this type of potential and most have as radial part either the Coulomb potential or the harmonic oscillator.…”

Section: Introductionmentioning

confidence: 99%

Non-relativistic and relativistic equations for the Kratzer potential plus a dipole in 2D systems

2019

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In this work, we study the wave equations in 2D Euclidian space for a new non-central potential consisting of a Kratzer term and a dipole term V (r, θ) = Qr −1 +Drr −2 +D θ cos(θ)r −2 . For Schrodinger equation, we obtain the analytical expressions of the energies and the wave functions of the system. For Klein-Gordon and Dirac equations, we do the study in both spin and pseudo-spin symmetries to get the eigenfunctions and the eigenvalues. We also study the dependence of energies on the parameters Dr and D θ . We find that the D θ term tends to dissociate the system, and thus counteracts the Coulomb binding effect, and that the Dr term can either amplify or decrease this effect according to its sign.

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“…Этот метод известен как обобщенное преобразование (ОП) [2]. Многие авторы внесли значительный вклад в конструирование (и реконструирование) полиномиальных ТРП [3], неполиномиальных потенциалов [4]- [9] и потенциалов кольцевого типа [10] с применением метода ОП.…”

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Построение Точно Решаемых Потенциалов В $D$-Мерном Уравнении Шредингера С Массой, Зависящей От Координат, При Помощи Метода Преобразований

Райбонгши¹,

Rajbongshi²,

Сингх³

et al. 2015

TMF

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Метод обобщенных преобразований применяется к радиальному уравнению Шредингера с постоянной массой, которому удовлетворяет сферически-симметричный центральный потенциал, с целью получения точно решаемых квантовых систем с массой, зависящей от координат, в пространстве произвольной размерности в нерелятивистском пределе. Метод включает в себя координатное преобразование с последующим функциональным преобразованием и набор подстановок для функции массы, который приводит к появлению точно решаемых квантовых систем с массами, зависящими от координат. Также показано, что упорядочение Жу-Кремера для значений нефиксированных параметров оказывается естественным для систем с радиально-симметричными функциями масс и центральным потенциалом. В качестве примера метод применяется к потенциалу Меннинга-Розена и потенциалу Морса при различных выборах функций массы. Указано также на применение метода к потенциалу Халтена.

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Systematic search of exactly solvable ring-shaped potential using the transformation method

Cited by 8 publications

References 42 publications

Schrödinger equation for non-pure dipole potential in 2D systems

Schrödinger equation for non-pure dipole potential in 2D systems

Non-relativistic and relativistic equations for the Kratzer potential plus a dipole in 2D systems

Построение Точно Решаемых Потенциалов В $D$-Мерном Уравнении Шредингера С Массой, Зависящей От Координат, При Помощи Метода Преобразований

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