New supersymmetric partners for the associated Lamé potentials

Fernández, J C David; Ganguly, Asish

doi:10.1016/j.physleta.2005.03.011

Cited by 14 publications

(33 citation statements)

References 20 publications

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“…To find Ψ, it is sufficient to solve just one of the Lamé equations in (3.12). Thus, for instance, take that of spin down component Two independent solutions ψ ± (y) of (3.13) can be found in a closed form [17] ψ ± (y) = H(y ± α) Θ(y) e ∓yζ(α) , α ∈ C, (3.14) where H(y) and Θ(y) are theta functions and ζ(α) is the Jacobi zeta function [20]. These theta functions satisfy Θ(y + 2K) = Θ(y) and H(y + 2K) = −H(y).…”

Section: Equation (33) Can Be Cast In the Formmentioning

confidence: 99%

Carbon nanotubes in an inhomogeneous transverse magnetic field: exactly solvable model

Jakubský¹,

Kuru²,

Negro³

2014

J. Phys. A: Math. Theor.

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A class of exactly solvable models describing carbon nanotubes in the presence of an external inhomogeneous magnetic field is considered. The framework of the continuum approximation is employed, where the motion of the charge carriers is governed by the Dirac-Weyl equation. The explicit solution of a particular example is provided. It is shown that these models possess nontrivial integrals of motion that establish N = 2 nonlinear supersymmetry in case of metallic and maximally semiconducting nanotubes. Remarkable stability of energy levels with respect to small fluctuations of longitudinal momentum is demonstrated.

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Section: Equation (33) Can Be Cast In the Formmentioning

confidence: 99%

Carbon nanotubes in an inhomogeneous transverse magnetic field: exactly solvable model

Jakubský¹,

Kuru²,

Negro³

2014

J. Phys. A: Math. Theor.

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“…In the intermediate region the reformulation of equation (2.18) is useful to solve the spectral problem. The crucial observation is that this equation may be transformed into the well-known associated Lamé equation [52][53][54][55][56][57] …”

Section: Expressions For Wave Functionsmentioning

confidence: 99%

“…But the other limit k → 0 may be considered as it allows the shrinking of the region (−x 0 , x 0 ) up to a finite interval (−1, 1). The general solutions of equation (2.21) for arbitrary energy E, which we need, was obtained only recently in Ref [57,58]. Here we will not describe the method of obtaining these solutions, but for readers' convenience, we have included a self-contained brief introduction about elliptic functions in Appendix A.…”

Section: Expressions For Wave Functionsmentioning

confidence: 99%

A new effective mass Hamiltonian and associated Lamé equation: bound states

Ganguly¹,

Ioffe²,

Nieto³

2006

J. Phys. A: Math. Gen.

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Abstract.A new quantum model with rational functions for the potential and effective mass is proposed in a stretchable region outside which both are constant. Starting from a generalized effective mass kinetic energy operator the matching and boundary conditions for the envelope wave functions are derived. It is shown that in a mapping to an auxiliary constant-mass Schrödinger picture one obtains one-period "associated Lamé" well bounded by two δ-wells or δ-barriers depending on the values of the ordering parameter β. The results for bound states of this new solvable model are provided for a wide variation of the parameters.

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“…integers are exactly solvable, in the sense that the stationary Schrödinger equation admits analytic solutions for any value of the energy parameter [3,4]. The initial motivation to look for this result was the need to implement supersymmetric quantum mechanics for generating new exactly solvable models (periodic and asymptotically periodic) [5,6,7,8,9,10].…”

Section: Introductionmentioning

confidence: 99%