Multistep DBT and regular rational extensions of the isotonic oscillator

Journal Article · Mon Oct 15 04:00:00 EDT 2012 · Annals of Physics (New York)

DOI:https://doi.org/10.1016/J.AOP.2012.07.004· OSTI ID:22157101

Grandati, Yves

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 DBTs are built on the excited states Riccati-Schroedinger (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 explicitly that these extensions inherit the shape invariance properties of the original potential. - Highlights: Black-Right-Pointing-Pointer Hamiltonian hierarchies via SUSY quantum partnership generalized to excited states. Black-Right-Pointing-Pointer Goes beyond the scope of the Crum and Krein-Adler theorems. Black-Right-Pointing-Pointer Complete proofs based on deconjugacy theorems and recurrency scheme. Black-Right-Pointing-Pointer Determinantal expressions for new exceptional Laguerre polynomials. Black-Right-Pointing-Pointer Proof of the hereditary character of the shape invariance.

• OSTI ID: 22157101
• Journal Information: Annals of Physics (New York), Journal Name: Annals of Physics (New York) Journal Issue: 10 Vol. 327; ISSN 0003-4916; ISSN APNYA6
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
EIGENSTATES
EXCITED STATES
HAMILTONIANS
LAGUERRE POLYNOMIALS
OSCILLATORS
POTENTIALS
QUANTUM MECHANICS
SCHROEDINGER EQUATION
SUPERSYMMETRY
TRANSFORMATIONS