Group theoretic approach to rationally extended shape invariant potentials

Abstract

The exact bound state spectrum of rationally extended shape invariant real as well as $PT$ symmetric complex potentials are obtained by using potential group approach. The generators of the potential groups are modified by introducing a new operator $U(x,J_3\pm 1/2)$ to express the Hamiltonian corresponding to these extended potentials in terms of Casimir operators. Connection between the potential algebra and the shape invariance is elucidated.

12 Pages, Latex

References in corpus (6)

• Infinitely many shape invariant potentials and new orthogonal polynomials
• Exceptional orthogonal polynomials, exactly solvable potentials and supersymmetry
• Solvable rational extensions of the isotonic oscillator
• Exceptional orthogonal polynomials and the Darboux transformation
• Dirac(-Pauli), Fokker-Planck equations and exceptional Laguerre polynomials
• Effect of Position-dependent Mass on Dynamical Breaking of Type B and Type X_2 N-fold Supersymmetry

Cited by in corpus (10)

• Parametric symmetries in exactly solvable real and P T symmetric complex potentials
• A class of exactly solvable rationally extended non-central potentials in Two and Three Dimensions
• Scattering amplitudes for the rationally extended P T symmetric complex potentials
• A class of exactly solvable rationally extended Calogero-Wolfes type 3-body problems
• A short note on "Group theoretic approach to rationally extended shape invariant potentials" [Annals of Physics 359, 46 (2015)]
• Rationally extended many-body truncated Calogero-Sutherland model
• Supersymmetry and Shape Invariance of exceptional orthogonal polynomials
• Solutions of (1+1)-dimensional Dirac equation associated with exceptional orthogonal polynomials and the parametric symmetry
• Generalized coherent states of exceptional Scarf-I potential: Their spatio-temporal and statistical properties
• Infinite families of shape invariant potentials with n parameters subject to translation