4 research outputs found
On the new translational shape invariant potentials
Recently, several authors have found new translational shape invariant
potentials not present in classic classifications like that of Infeld and Hull.
For example, Quesne on the one hand and Bougie, Gangopadhyaya and Mallow on the
other have provided examples of them, consisting on deformations of the
classical ones. We analyze the basic properties of the new examples and observe
a compatibility equation which has to be satisfied by them. We study particular
cases of such equation and give more examples of new translational shape
invariant potentials.Comment: 9 pages, uses iopart10.clo, version
A short note on “Group theoretic approach to rationally extended shape invariant potentials” [Ann. Phys. 359 (2015) 46–54]
It is proved the equivalence of the compatibility condition of Ramos (2011, 2012) with a condition found in Yadav et al. (2015). The link of Shape Invariance with the existence of a Potential Algebra is reinforced for the rationally extended Shape Invariant potentials. Some examples on X1 and Xl Jacobi and Laguerre cases are given
Group theoretical approach to the intertwined Hamiltonians
We show that the finite difference B\"acklund formula for the Schr\"odinger
Hamiltonians is a particular element of the transformation group on the set of
Riccati equations considered by two of us in a previous paper. Then, we give a
group theoretical explanation to the problem of Hamiltonians related by a first
order differential operator. A generalization of the finite difference
algorithm relating eigenfunctions of {\emph three} different Hamiltonians is
found, and some illustrative examples of the theory are analyzed, finding new
potentials for which one eigenfunction and its corresponding eigenvalue is
exactly known