Exactly solvable associated Lamé potentials and supersymmetric transformations

Fernández, J C David; Ganguly, Asish

doi:10.1016/j.aop.2006.07.011

Cited by 20 publications

(23 citation statements)

References 28 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Although the previous approach allows to find the solutions of equations (3)(4) for some integer values of the parameters (m, ℓ), however it is not completely systematic. In order to fill the gap, let us use the Frobenius method for solving (4) [4]. With this aim, let us make the following changes:…”

Section: General Solutions Of the Associated Lamé Equationmentioning

confidence: 99%

“…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%

See 1 more Smart Citation

Supersymmetric partners for the associated Lamé potentials

Fernandez

Ganguly

2010

Phys. Atom. Nuclei

View full text Add to dashboard Cite

show abstract

Section: General Solutions Of the Associated Lamé Equationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Supersymmetric partners for the associated Lamé potentials

Fernandez

Ganguly

2010

Phys. Atom. Nuclei

View full text Add to dashboard Cite

show abstract

“…It is interesting to observe that in supersymmetric quantum mechanics, [78][79][80][81][82] such form for the potential u is linked with its isospectral (almost) partner potentialũ = W 2 − W x , the quantity W being termed as superpotential. 83 In the nonlinear field, such a transformation yields a new nonlinear equation in the variable W (x, t), known as mKdV equation, in which Galilean invariance is lost.…”

Section: Introductionmentioning

confidence: 99%

Generalized Korteweg-de Vries equation induced from position-dependent effective mass quantum models and mass-deformed soliton solution through inverse scattering transform

Ganguly

Das

2014

Journal of Mathematical Physics

View full text Add to dashboard Cite

We consider one-dimensional stationary position-dependent effective mass quantum model and derive a generalized Korteweg-de Vries (KdV) equation in (1 + 1) dimension through Lax pair formulation, one being the effective mass Schrödinger operator and the other being the time-evolution of wave functions. We obtain an infinite number of conserved quantities for the generated nonlinear equation and explicitly show that the new generalized KdV equation is an integrable system. Inverse scattering transform method is applied to obtain general solution of the nonlinear equation, and then N-soliton solution is derived for reflectionless potentials. Finally, a special choice has been made for the variable mass function to get massdeformed soliton solution. The influence of position and time-dependence of mass and also of the different representations of kinetic energy operator on the nature of such solitons is investigated in detail. The remarkable features of such solitons are demonstrated in several interesting figures and are contrasted with the conventional KdV-soliton associated with constant-mass quantum model. C 2014 AIP Publishing LLC. [http://dx.doi.org/10.1063/1.4900895]In this equation T EM (x) is the EM kinetic energy operator and ψ(x) is known as envelope wavefunction. Due to the non-commutativity of momentum operator p ≡ − i ∂ x and the effective mass operator m(x), an infinite number of representation is possible for the kinetic energy operator. It is well-known that a hermitian form is induced by a general two-parameter family 37(1.2)Note that the form (1.2) is not the most general form. Other non-hermitian forms exist. However, to the best of our knowledge, it is the general form among hermitian family. It has to be mentioned that although different possible representations are covered in (1.2), some special forms attract much a) Electronic addresses:

show abstract

“…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.

View full text Add to dashboard Cite

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.

show abstract

Exactly solvable associated Lamé potentials and supersymmetric transformations

Cited by 20 publications

References 28 publications

Supersymmetric partners for the associated Lamé potentials

Supersymmetric partners for the associated Lamé potentials

Generalized Korteweg-de Vries equation induced from position-dependent effective mass quantum models and mass-deformed soliton solution through inverse scattering transform

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

Contact Info

Product

Resources

About