First-Order SUSY Partners of the Trigonometric Pöschl-Teller Potential

Contreras-Astorga, Alonso; Fernández, J C David

doi:10.1063/1.2825131

Cited by 4 publications

(3 citation statements)

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“…Let us classify the first-order SUSY partners according to the changes induced on the initial spectrum. Three different cases have been identified [16].…”

Section: First-order Susy Partnersmentioning

confidence: 99%

“…In the case that the intertwining operator is of first order the procedure can be implemented by using as seed one Schrödinger solution which factorization energy is less than or equal to the ground state energy of H [2][3][4][5][6][7][8][9][10][11][12][13][14][15][16]. In order to surpass successfully this restriction, one needs to use interwining operators at least of second order [17][18][19][20][21][22][23][24][25][26][27].…”

Section: Introductionmentioning

confidence: 99%

“…In order to complete the scheme, it is important to apply them to cases where the x-domain is a finite interval, let us say [x l , x r ]. An example of this kind, to be explored in detail in this paper, is the trigonometric Pöschl-Teller potential [16,[27][28][29]. This is closely related to several potentials widely used in molecular and solid state physics [28].…”

Section: Introductionmentioning

confidence: 99%

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Supersymmetric partners of the trigonometric Pöschl–Teller potentials

Contreras-Astorga¹,

C.²

2008

J. Phys. A: Math. Theor.

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The first and second-order supersymmetry transformations are used to generate Hamiltonians with known spectra departing from the trigonometric Pöschl-Teller potentials. The several possibilities of manipulating the initial spectrum are fully explored, and it is shown how to modify one or two levels, or even to leave the spectrum unaffected. The behavior of the new potentials at the boundaries of the domain is studied.

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“…Let us classify the first-order SUSY partners according to the changes induced on the initial spectrum. Three different cases have been identified [16].…”

Section: First-order Susy Partnersmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Supersymmetric partners of the trigonometric Pöschl–Teller potentials

Contreras-Astorga¹,

C.²

2008

J. Phys. A: Math. Theor.

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Arbitrary‐order darboux transformations for position‐dependent mass schrödinger equations with noncentral potential

Schulze-Halberg¹,

Zamora-Gallardo

Peña

2009

Int J of Quantum Chemistry

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Trends in Supersymmetric Quantum Mechanics

David²

2019

Integrability, Supersymmetry and Coherent States

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Along the years, supersymmetric quantum mechanics (SUSY QM) has been used for studying solvable quantum potentials. It is the simplest method to build Hamiltonians with prescribed spectra in the spectral design. The key is to pair two Hamiltonians through a finite order differential operator. Some related subjects can be simply analyzed, as the algebras ruling both Hamiltonians and the associated coherent states. The technique has been applied also to periodic potentials, where the spectra consist of allowed and forbidden energy bands. In addition, a link with nonlinear second-order differential equations, and the possibility of generating some solutions, can be explored. Recent applications concern the study of Dirac electrons in graphene placed either in electric or magnetic fields, and the analysis of optical systems whose relevant equations are the same as those of SUSY QM. These issues will be reviewed briefly in this paper, trying to identify the most important subjects explored currently in the literature. KeywordsSupersymmetric quantum mechanics • Coherent states • Painlevé equations • Painlevé transcendents • Polynomial Heisenberg algebras • Factorization method • Exact solutions • Spectral design • Graphene Dedicated to my dear friend and colleague Véronique Hussin. D. J. Fernández C ( )

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First-Order SUSY Partners of the Trigonometric Pöschl-Teller Potential

Cited by 4 publications

References 0 publications

Supersymmetric partners of the trigonometric Pöschl–Teller potentials

Supersymmetric partners of the trigonometric Pöschl–Teller potentials

Arbitrary‐order darboux transformations for position‐dependent mass schrödinger equations with noncentral potential

Trends in Supersymmetric Quantum Mechanics

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