Parametric symmetries in exactly solvable real and P T symmetric complex potentials
arXiv:1510.01666 · doi:10.1063/1.4954330
Abstract
In this paper, we discuss the parametric symmetries in different exactly solvable systems characterized by real or complex P T symmetric potentials. We focus our at- tention on the conventional potentials such as the generalized Poschl Teller (GPT), o Scarf-I and P T symmetric Scarf-II which are invariant under certain parametric transformations. The resulting set of potentials are shown to yield a completely dif- ferent behavior of the bound state solutions. Further the supersymmetric (SUSY) partner potentials acquire different forms under such parametric transformations leading to new sets of exactly solvable real and P T symmetric complex potentials. These potentials are also observed to be shape invariant (SI) in nature. We subse- quently take up a study of the newly discovered rationally extended SI Potentials, corresponding to the above mentioned conventional potentials, whose bound state solutions are associated with the exceptional orthogonal polynomials (EOPs). We discuss the transformations of the corresponding Casimir operator employing the properties of the so(2,1) algebra.
22 pages, Latex, No figs
References in corpus (12)
- Making Sense of Non-Hermitian Hamiltonians
- Infinitely many shape invariant potentials and new orthogonal polynomials
- Exceptional orthogonal polynomials, exactly solvable potentials and supersymmetry
- Solvable Rational Potentials and Exceptional Orthogonal Polynomials in Supersymmetric Quantum Mechanics
- 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
- Group theoretic approach to rationally extended shape invariant potentials
- Scattering amplitudes for the rationally extended P T symmetric complex potentials
- Ladder operators for solvable potentials connected with exceptional orthogonal polynomials
- Comment on `Supersymmetry, PT-symmetry and spectral bifurcation'
Cited by in corpus (11)
- Deconfinement to Confinement as PT phase transition
- A class of exactly solvable rationally extended non-central potentials in Two and Three Dimensions
- New scattering features in non-Hermitian space fractional quantum mechanics
- 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
- Exactness of Semiclassical Quantization Rule for Broken Supersymmetry
- Supersymmetry and Shape Invariance of exceptional orthogonal polynomials
- Solutions of (1+1)-dimensional Dirac equation associated with exceptional orthogonal polynomials and the parametric symmetry
- The massless Dirac-Weyl equation with deformed extended complex potentials