Exact supersymmetry in the nonrelativistic hydrogen atom

Tangerman, R.D.; Tjon, J.A.

doi:10.1103/physreva.48.1089

Cited by 21 publications

(19 citation statements)

References 15 publications

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“…Because of the significant analytical and computational ramifications, and motivated by the future study of more complex electronic systems, we here apply our multi-dimensional generalization of SUSY-QM to the hydrogen atom in full three-dimensional detail. This is of interest because, until now, the standard application of SUSY-QM to the hydrogen atom required that we first separate out the angular degrees of freedom -effectively reducing the problem to a one-dimensional treatment [Kirchberg et al (2003); Lahiri et al (1987); Tangerman & Tjon (1993)]. With our vector superpotential approach, one can deal with the full three-dimensional nature of the hydrogen atom.…”

Section: Electronic Structure Of Atoms: Hydrogen and Heliummentioning

confidence: 99%

Generalized Non-Relativistic Supersymmetric Quantum Mechanics

Markovich¹,

Biamonte²,

Bittner³

et al. 2012

Measurements in Quantum Mechanics

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Section: Electronic Structure Of Atoms: Hydrogen and Heliummentioning

confidence: 99%

Generalized Non-Relativistic Supersymmetric Quantum Mechanics

Markovich¹,

Biamonte²,

Bittner³

et al. 2012

Measurements in Quantum Mechanics

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“…In addition to the above approaches, there is an independent powerful approach i.e., potential algebra (or group theoretical) approach [35,36,37,38,39,40,44,45], by which one can obtain the exact spectrum of some of these exactly solvable potentials. Alhassid et.al.…”

Section: Introductionmentioning

confidence: 99%

Group theoretic approach to rationally extended shape invariant potentials

et al. 2015

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The exact bound state spectrum of rationally extended shape invariant real as well as P T symmetric complex potentials are obtained by using potential group approach. The generators of the potential groups are modified by introducing a new operator U (x, J 3 ± 1 2 ) to express the Hamiltonian corresponding to these extended potentials in terms of Casimir operators. Connection between the potential algebra and the shape invariance is elucidated.

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“…In fact, our studies are based on the supersymmetric quantum mechanics and Refs. [2][3][4][5][6][7][8][9][10][11]. In Ref.…”

Section: Introductionmentioning

confidence: 99%

Supersymmetry approaches to the radial bound states of the hydrogen‐like atoms

Chenaghlou

Fakhri

2004

Int J of Quantum Chemistry

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ABSTRACT:Introducing the associated Bessel polynomials in terms of two nonnegative integers, we factorize their corresponding differential equation into a product of first-order differential operators by four different ways as shape invariance equations. Then, the radial part of the bound states of the Schrö dinger equation of a hydrogen-like atom is derived using one of the factorization methods in the framework of supersymmetric quantum mechanics. In this approach, we regenerate the radial bound states and their corresponding spectrum, which are consistent with the well-known facts. Based on the generalization of the supersymmetry idea, we shall show that two hydrogen-like atoms with the same energy of the electron possess three extra supersymmetric structures in addition to an ordinary one.

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Exact supersymmetry in the nonrelativistic hydrogen atom

Cited by 21 publications

References 15 publications

Generalized Non-Relativistic Supersymmetric Quantum Mechanics

Generalized Non-Relativistic Supersymmetric Quantum Mechanics

Group theoretic approach to rationally extended shape invariant potentials

Supersymmetry approaches to the radial bound states of the hydrogen‐like atoms

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