Exact numerical solutions of the Schrödinger equation for a two-dimensional exciton in a constant magnetic field of arbitrary strength

Hoang-Do, Ngoc-Tram; Pham, Dang-Lan; Le, Van-Hoang

doi:10.1016/j.physb.2013.04.040

Cited by 13 publications

(12 citation statements)

References 24 publications

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“…This method is based totally on algebraic calculations and has been used for some two dimensional problems (for example, see Refs. 20,21,25,[28][29][30]. The main idea of the FK operator method of solving the Schrödinger equation is to use the basis set of wave functions of the harmonic oscillator with the frequency ω, serving as a free parameter which is useful for controlling the convergence rate of the solutions.…”

Section: Exact Solutions For Specific Geometry Valuesmentioning

confidence: 99%

“…However, the two-dimensional case is not trivial due to its symmetry. The inspiration to consider the two-dimensional case is the connection between the two-dimensional hydrogen atom in the magnetic field and the two-dimensional purely sextic double-well problem by the Levi-Civita transformation [20][21][22] since the former has exact solutions investigated in Ref. 23.…”

Section: Introductionmentioning

confidence: 99%

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Exact analytical solutions of the Schrödinger equation for a two dimensional purely sextic double-well potential

Hoang

2018

Journal of Mathematical Physics

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Exact analytical solutions of the Schrödinger equation for a two-dimensional purely sextic double-well potential are proved to exist for a denumerably infinite set of the geometry parameter of the well. First, the geometry values which allow exact solutions are determined. Then, explicit wave functions and corresponding energies are calculated for the allowed geometry values. Concrete exact solutions are given for the principal quantum number n up to 10. Moreover, some interesting rules for the obtained exact analytical solutions are also given; particularly, the number of negative energy levels for a given geometry parameter is obtained. For analyzing the obtained exact solutions and for their classification by quantum number, we also use numerical calculations by the Feranchuk-Komarov operator method. Published by AIP Publishing. https://doi

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Section: Exact Solutions For Specific Geometry Valuesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Exact analytical solutions of the Schrödinger equation for a two dimensional purely sextic double-well potential

Hoang

2018

Journal of Mathematical Physics

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“…The double-well anharmonic oscillator (DWAO) holds a great importance because of its relation to many problems of quantum chemistry and field theory [1][2][3][4]. Dai-Nam Le et al was studied the Schrödinger equation for the purely sextic double-well potential problem in twodimensional space by wave function ansatz method for analytical approach and by Feranchuk-Komarov operator method for numerical approach [1].…”

Section: Introductionmentioning

confidence: 99%

A Theoretical Investigation of the Schrödinger Equation for a Modified Two Dimensional Purely Sextic Double-Well Potential

Maireche¹

2021

Yanbu Journal of Engineering and Science

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A theoretical analytical investigation for the exact solvability of non-relativistic quantum spectrum systems, at low energy for modified two-dimensional purely sextic double-well potential (2D-modified sextic DWAO potential) is discussed, by means Bopp's shift method, instead to solving deformed Schrödinger equation with star product, in the framework of both noncommutativite two dimensional real space and phase (NC: 2D-RSP), the exact corrections for lowest excitations are found straightforwardly for interactions in one-electron atoms by means of the standard perturbation theory for three special cases. Furthermore, the obtained corrections of energies are depended on the four infinitesimals parameters (  ,  ) and ( ,  ),

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“…Properties of model two-dimensional hydrogenic systems immersed in a magnetic field have been investigated for several decades within the frameworks of nonrelativistic and relativistic [32][33][34][35][36][37][38][39][40][41][42][43] quantum mechanics. Besides of being interesting from a purely theoretical point of view, results of such studies are also important for understanding various aspects of physics of lowdimensional semiconductors [1][2][3][6][7][8]10,12,15,18,26] and of graphene [44][45][46][47][48][49][50][51]. The subject is still far from being exhausted, and further research in this area, especially the one based on the use of analytical methods, is certainly demanded.…”

Section: Introductionmentioning

confidence: 99%

Relativistic two-dimensional hydrogen-like atom in a weak magnetic field

Szmytkowski

2019

Annals of Physics

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A two-dimensional (2D) hydrogen-like atom with a relativistic Dirac electron, placed in a weak, static, uniform magnetic field perpendicular to the atomic plane, is considered. Closed forms of the first-and second-order Zeeman corrections to energy levels are calculated analytically, within the framework of the Rayleigh-Schrödinger perturbation theory, for an arbitrary electronic bound state. The second-order calculations are carried out with the use of the Sturmian expansion of the two-dimensional generalized radial Dirac-Coulomb Green function derived in the paper. It is found that, in contrast to the case of the three-dimensional atom [P. Stefańska, Phys. Rev. A 92 (2015) 032504], in two spatial dimensions atomic magnetizabilities (magnetic susceptibilities) are expressible in terms of elementary algebraic functions of a nuclear charge and electron quantum numbers. The problem considered here is related to the Coulomb impurity problem for graphene in a weak magnetic field.

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Exact numerical solutions of the Schrödinger equation for a two-dimensional exciton in a constant magnetic field of arbitrary strength

Cited by 13 publications

References 24 publications

Exact analytical solutions of the Schrödinger equation for a two dimensional purely sextic double-well potential

Exact analytical solutions of the Schrödinger equation for a two dimensional purely sextic double-well potential

A Theoretical Investigation of the Schrödinger Equation for a Modified Two Dimensional Purely Sextic Double-Well Potential

Relativistic two-dimensional hydrogen-like atom in a weak magnetic field

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