Quasi-Exact Solvability of Planar Dirac Electron in Coulomb and Magnetic Fields

Chiang, C. H.; Ho, Choon‐Lin

doi:10.1142/s0217732305016452

Cited by 5 publications

(9 citation statements)

References 15 publications

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“…On the other hand, there exists a Dirac system which has no intrinsic SUSY structure but is quasi-(exactly) solvable [31]. One of the peculiar aspects of the system is that the underlying algebraic structure is the Lie superalgebra osp(2|2) instead of sl(2) [32]. Hence, it is interesting to clarify whether or not we are able to embed N -fold SUSY into such a system, too.…”

Section: Discussion and Summarymentioning

confidence: 99%

Simultaneous ordinary and type A N-fold supersymmetries in Schrödinger, Pauli, and Dirac equations

Ho¹,

Tanaka²

2006

Annals of Physics

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We investigate physical models which possess simultaneous ordinary and type A N -fold supersymmetries, which we call type A (N , 1)-fold supersymmetry. Inequivalent type A (N , 1)-fold supersymmetric models with real-valued potentials are completely classified. Among them, we find that a trigonometric Rosen-Morse type and its elliptic version are of physical interest. We investigate various aspects of these models, namely, dynamical breaking and interrelation between ordinary and N -fold supersymmetries, shape invariance, quasi-solvability, and an associated algebra which is composed of one bosonic and four fermionic operators and dubbed type A (N , 1)-fold superalgebra. As realistic physical applications, we demonstrate how these systems can be embedded into Pauli and Dirac equations in external electromagnetic fields.

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Section: Discussion and Summarymentioning

confidence: 99%

Simultaneous ordinary and type A N-fold supersymmetries in Schrödinger, Pauli, and Dirac equations

Ho¹,

Tanaka²

2006

Annals of Physics

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“…More recently the Dirac-Pauli equation was reconsidered [6] in the context of neutral particle interacting with an electromagnetic field and shown to be strongly related to the case of a Dirac oscillator. A similar problem was emphasized is 1+2 dimensions in [7]. With suitable form of the radial potentials, the corresponding Dirac equation can be quasi exactly solvable.…”

Section: Introductionmentioning

confidence: 87%

“…Here we consider the case of a planar Dirac electron in Coulomb plus magnetic field. This case was studied in [7,11]. In the general framework of Eq.…”

Section: Quasi Exactly Solvable Cases 41 Planar Casementioning

confidence: 99%

Dirac Oscillators and Quasi-Exactly Solvable Operators

Brihaye

Nininahazwe

2005

Mod. Phys. Lett. A

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The Dirac equation is considered in the background of potentials of several types, namely scalar and vector-potentials as well as "Dirac-oscillator" potential or some of its generalisations. We investigate the radial Dirac equation within a quite general spherically symmetric form for these potentials and we analyse some exactly and quasi exactly solvable properties of the underlying matricial linear operators. 0

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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].…”

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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Quasi-Exact Solvability of Planar Dirac Electron in Coulomb and Magnetic Fields

Cited by 5 publications

References 15 publications

Simultaneous ordinary and type A N-fold supersymmetries in Schrödinger, Pauli, and Dirac equations

Simultaneous ordinary and type A N-fold supersymmetries in Schrödinger, Pauli, and Dirac equations

Dirac Oscillators and Quasi-Exactly Solvable Operators

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

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