Physics – Mathematical Physics
Scientific paper
2011-08-23
Physics
Mathematical Physics
Scientific paper
In some recent articles we developed a new systematic approach to generate solvable rational extensions of primary translationally shape invariant potentials. In this generalized SUSY QM partnership, the DBT are built on the excited states Riccati-Schr\"odinger (RS) functions regularized via specific discrete symmetries of the considered potential. In the present paper, we prove that this scheme can be extended in a multistep formulation. Applying this scheme to the isotonic oscillator, we obtain new towers of regular rational extensions of this potential which are strictly isospectral to it. We give explicit expressions for their eigenstates which are associated to the recently discovered exceptional Laguerre polynomials and show explicitely that these extensions inherit of the shape invariance properties of the original potential.
No associations
LandOfFree
Multistep DBT and regular rational extensions of the isotonic oscillator does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Multistep DBT and regular rational extensions of the isotonic oscillator, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Multistep DBT and regular rational extensions of the isotonic oscillator will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-66853