2008
DOI: 10.1088/1751-8113/41/47/475303
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Supersymmetric partners of the trigonometric Pöschl–Teller potentials

Abstract: 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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Cited by 42 publications
(51 citation statements)
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“…In one-dimensional systems, strict isospectrality may be present in the first-order systems (broken SUSY) when the factorization energy E is smaller than the ground-state energy of the starting Hamiltonian [7,8]. In such a context, the potential and eigenfunctions of the partner Hamiltonian are known in terms of analytic expressions, which, however, may be a good deal more complicated than the corresponding ones of the initial Hamiltonian [9]. Interestingly one can look for extensions to higher-order SUSY theories by resorting to higher-derivative versions of the factorization operators.…”
Section: Introductionmentioning
confidence: 99%
“…In one-dimensional systems, strict isospectrality may be present in the first-order systems (broken SUSY) when the factorization energy E is smaller than the ground-state energy of the starting Hamiltonian [7,8]. In such a context, the potential and eigenfunctions of the partner Hamiltonian are known in terms of analytic expressions, which, however, may be a good deal more complicated than the corresponding ones of the initial Hamiltonian [9]. Interestingly one can look for extensions to higher-order SUSY theories by resorting to higher-derivative versions of the factorization operators.…”
Section: Introductionmentioning
confidence: 99%
“…Suppose now that V 0 (x) is given; to determine V 2 (x) and γ (x) we need to find a solution η(x) to the nonlinear differential equation (17). This is done through the ansatz…”
Section: Second-order Supersymmetric Quantum Mechanicsmentioning
confidence: 99%
“…SUSY techniques have been applied successfully to several one-dimensional Hamiltonians, e.g., the harmonic oscillator, infinite well and Pöschl-Teller potentials (trigonometric or hyperbolic) [6,[11][12][13][14][15][16][17]. For these systems the generic discrete energy level E n is a secondorder polynomial of the index n. This implies that there is an intrinsic algebraic structure (IAS) of Lie type involving the number, annihilation and creation operators, since the commutator between the ladder operators, which coincides with E n+1 − E n , is linear in n [16].…”
Section: Introductionmentioning
confidence: 99%
“…To apply it we need a solvable initial system and at least one of its solutions, as a result a new system, often referred as SUSY partner, and its solutions are generated [9,11,16]. This tool has been applied to a large variety of quantum interactions such as the harmonic oscillator [15], the hydrogen atom [12,21], the Pöschl-Teller potentials [6], among many others. Moreover, it has been possible to extend the SUSY formalism so it can be used to find solutions of different kind of equations like the FokkerPlanck equation [22,24], the time dependent Schrödinger equation [3], mass position dependent Schrödinger equation [13], Painlevé equations [4] and Dirac equations [5,7,8,10,14,18,20].…”
Section: Introductionmentioning
confidence: 99%