C Quesne 2008 J. Phys. A: Math. Theor. 41 392001 doi:10.1088/1751-8113/41/39/392001
C Quesne
Show affiliationsWe construct two new exactly solvable potentials giving rise to bound-state solutions to the Schrödinger equation, which can be written in terms of the recently introduced Laguerre- or Jacobi-type X1 exceptional orthogonal polynomials. These potentials, extending either the radial oscillator or the Scarf I potential by the addition of some rational terms, turn out to be translationally shape invariant as their standard counterparts and isospectral to them.
03.65.Ge Solutions of wave equations: bound states
02.10.De Algebraic structures and number theory
03.65.Ta Foundations of quantum mechanics; measurement theory
15A18 Eigenvalues, singular values, and eigenvectors
Issue 39 (3 October 2008)
Received 8 July 2008, in final form 8 August 2008
Published 29 August 2008
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