Polynomial Heisenberg algebras

Carballo, Juan Manuel; C., David J. Fernández; Negro, J.; Nieto, L. M.

doi:10.1088/0305-4470/37/43/022

Cited by 78 publications

(142 citation statements)

References 36 publications

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“…It is important to remark that, in a sense, the graphene coherent states remind the multiphoton coherent states [28,29,30,31,32,33], which appear from realizations of the Polynomial Heisenberg Algebras (PHA) for the harmonic oscillator [24,25,26,34,35,36]. In that formalism, the Hilbert space decomposes as a direct sum of m orthogonal subspaces, on each of which it is possible to construct the corresponding coherent states as superpositions of standard coherent states, while in the case of this paper the minimum energy states can be isolated from the remaining Hilbert subspace, depending on the values taken by f (n).…”

Section: Discussionmentioning

confidence: 99%

Graphene coherent states

Díaz-Bautista

2017

Eur. Phys. J. Plus

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In this paper we will construct the coherent states for a Dirac electron in graphene placed in a constant homogeneous magnetic field which is orthogonal to the graphene surface. First of all, we will identify the appropriate annihilation and creation operators. Then, we will derive the coherent states as eigenstates of the annihilation operator, with complex eigenvalues. Several physical quantities, as the Heisenberg uncertainty product, probability density and mean energy value, will be as well explored.

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Section: Discussionmentioning

confidence: 99%

Graphene coherent states

Díaz-Bautista

2017

Eur. Phys. J. Plus

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“…To perform the higher-order SUSY transformations onto this potential we will explore once again the factorization method [8,31,32]. The radial oscillator Hamiltonian can be factorized directly in four different ways.…”

Section: Example 2 the Radial Oscillatormentioning

confidence: 99%

“…In order to perform the SUSY transformations, we need to find the general solution of the Schrödinger equation for any factorization energy , which is given by [8,33,34] …”

Section: Example 2 the Radial Oscillatormentioning

confidence: 99%

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Supersymmetric quantum mechanics and Painlevé equations

Bermúdez

Fernández

2014

AIP Conference Proceedings

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In these lecture notes we shall study first the supersymmetric quantum mechanics (SUSY QM), specially when applied to the harmonic and radial oscillators. In addition, we will define the polynomial Heisenberg algebras (PHA), and we will study the general systems ruled by them: for zero and first order we obtain the harmonic and radial oscillators, respectively; for second and third order PHA the potential is determined by solutions to Painlevé IV (PIV) and Painlevé V (PV) equations. Taking advantage of this connection, later on we will find solutions to PIV and PV equations expressed in terms of confluent hypergeometric functions. Furthermore, we will classify them into several solution hierarchies, according to the specific special functions they are connected with.

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“…The underlying algebraic structure for the SUSY partners of the truncated oscillator was as well analyzed, becoming a deformation of the Heisenberg-Weyl algebra known as polynomial Heisenberg algebra [18,[30][31][32].…”

Section: Introductionmentioning

confidence: 99%

SUSY partners of the truncated oscillator, Painlevé transcendents and Bäcklund transformations

C.¹,

Morales-Salgado²

2016

J. Phys. A: Math. Theor.

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In this work the supersymmetric technique is applied to the truncated oscillator to generate Hamiltonians ruled by second and third-order polynomial Heisenberg algebras, which are connected to the Painlevé IV and Painlevé V equations respectively. The aforementioned connection is exploited to produce particular solutions to both non-linear differential equations and the Bäcklund transformations relating them.

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Polynomial Heisenberg algebras

Cited by 78 publications

References 36 publications

Graphene coherent states

Graphene coherent states

Supersymmetric quantum mechanics and Painlevé equations

SUSY partners of the truncated oscillator, Painlevé transcendents and Bäcklund transformations

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