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- Title
Shape invariant rational extensions and potentials related to exceptional polynomials.
- Authors
Sree Ranjani, S.; Sandhya, R.; Kapoor, A. K.
- Abstract
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 construct infinite sets of generalized potentials with exceptional polynomials as solutions. The method is simple and transparent and is elucidated using the radial oscillator and the trigonometric Pöschl-Teller potentials. For the case of radial oscillator, in addition to the known rational extensions, we construct two infinite sets of rational extensions, which seem to be less studied. Explicit expressions of the generalized infinite set of potentials and the corresponding solutions are presented. For the trigonometric Pöschl-Teller potential, our analysis points to the possibility of several rational extensions beyond those known in literature.
- Subjects
INVARIANTS (Mathematics); POLYNOMIALS; DEFORMATIONS (Mechanics); INFINITY (Mathematics); POSCHL-Teller potential
- Publication
International Journal of Modern Physics A: Particles & Fields; Gravitation; Cosmology; Nuclear Physics, 2015, Vol 30, Issue 24, p-1
- ISSN
0217-751X
- Publication type
Article
- DOI
10.1142/S0217751X15501468