Related papers: Reply to 'Comment on "Relativistic shape invariant…

Benenti et al. recently submitted a Comment (arXiv:0912.3667) on our work "Coherent Ratchets in Driven Bose-Einstein condensates". We show that the main claim of the Comment is wrong, and correct some other misunderstandings presented…

We present a novel technique to obtain relativistic corrections to the central force problem in the Lagrangian formulation, using a generalized potential energy function. We derive a general expression for a generalized potential energy…

Second order supersymmetric approach is taken to the system describing motion of a quantum particle in a potential endowed with position-dependent effective mass. It is shown that the intertwining relations between second order partner…

In supersymmetric quantum mechanics, exact-solvability of one-dimensional quantum systems can be classified only with an additional assumption of integrability, the so-called shape invariance condition. In this paper we show that in the…

After the rejection of their comment [arXiv:cond-mat/0609399v1] to our Phys. Rev. Lett. {\bf 97}, 100601 (2006), the Authors informed us that an extended version of their comment is going to be published in a different journal under the…

An algebro-operator approach, called shape invariant potential method, of constructing generalized coherent states for photon-added particle system is presented. Illustration is given on Poschl-Teller potential.

We find new families of shape invariant potentials depending on n>=1 parameters subject to translation by the inclusion of non-trivial invariants. New dependencies of the spectra are found, and it opens the door to the engineering of…

We show that the method developed by Gangopadhyaya, Mallow, and their coworkers to deal with (translationally) shape invariant potentials in supersymmetric quantum mechanics and consisting in replacing the shape invariance condition, which…

In this paper, we show that an attempt to construct shape invariant extensions of a known shape invariant potential leads to, apart from a shift by a constant, the well known technique of isospectral shift deformation. Using this, we…

We have reviewed the comment in [3], posted on arXiv.org concerning our recent work in [1]. We reply to the comment in this paper.

Using the underlying algebraic structures of Natanzon potentials, we discuss conditions that generate shape invariant potentials. In fact, these conditions give all the known shape invariant potentials corresponding to a translational…

We give two conditionally exactly solvable inverse power law potentials whose linearly independent solutions include a sum of two confluent hypergeometric functions. We notice that they are partner potentials and multiplicative shape…

In this letter we study a class of symmetries of the new translational extended shape invariant potentials. It is proved that a generalization of a compatibility condition introduced in a previous article is equivalent to the usual shape…

The supersymmetry based semiclassical method (SWKB) is known to produce exact spectra for conventional shape invariant potentials. In this paper we prove that this exactness follows from their additive shape invariance.

Motivated by the shape invariance condition in supersymmetric quantum mechanics, we develop an algebraic framework for shape invariant Hamiltonians with a general change of parameters. This approach involves nonlinear generalizations of Lie…

We examine shape invariant potentials (excluding those that are obtained by scaling) in supersymmetric quantum mechanics from the stand-point of periodic orbit theory. An exact trace formula for the quantum spectra of such potentials is…

This paper identifies a new class of shape invariant models. These models are based on extensions of conventional quantum mechanics that satisfy a string-motivated minimal length uncertainty relation. An important feature of our…

It is shown that the question raised in Section 5.7 of [1] has an affirmative answer.

We obtain pointwise estimates for solutions of semilinear parabolic equations with a potential on connected domains both of $\mathbb R^n$ and of general Riemannian manifolds.

We extensively investigate two-step shape invariance in the framework of N-fold supersymmetry. We first show that any two-step shape-invariant system possesses type A 2-fold supersymmetry with an intermediate Hamiltonian and thus has…