Shape invariant potentials with PT symmetry

Abstract

Suitable complexification of the well known solvable oscillators in one dimension is shown to give the four exactly solvable models which combine the shape- and PT-invariance. In version v2 the result is extended of the s-wave shape-invariant forces.

version 1: 5 pages, Latex (already published: J. Phys. A: Math. Gen. 33 (2000) L61-2; version 2: 28 pages of a review-type update prepared as a text of a proposed seminar (ATOMKI, Debrecen, presumably this week)

References in corpus (4)

• A new PT symmetric complex Hamiltonian with a real spectra
• Exact solution for Morse oscillator in PT-symmetric quantum mechanics
• Complex Square Well --- A New Exactly Solvable Quantum Mechanical Model
• Non-Hermitian matrix description of the PT symmetric anharmonic oscillators

Cited by in corpus (36)

• Making Sense of Non-Hermitian Hamiltonians
• Nonlinear waves in $\mathcal{P}\mathcal{T}$-symmetric systems
• sl(2, C) as a complex Lie algebra and the associated non-Hermitian Hamiltonians with real eigenvalues
• Integrable $\mathcal{P}T$-symmetric local and nonlocal vector nonlinear Schrödinger equations: a unified two-parameter model
• PT symmetric square well
• Pseudo-Hermiticity of Hamiltonians under imaginary shift of the co-ordinate : real spectrum of complex potentials
• Nonlinear localized modes in PT-symmetric Rosen-Morse potential well
• Spatial solitons and stability in self-focusing and defocusing Kerr nonlinear media with generalized PT-symmetric Scarff-II potentials
• Non-Hermitian Hamiltonians with real and complex eigenvalues in a Lie-algebraic framework
• Numerical Evidence that the Perturbation Expansion for a Non-Hermitian $\mathcal{P}\mathcal{T}$-Symmetric Hamiltonian is Stieltjes
• The Coulomb - harmonic oscillator correspondence in PT-symmetric quantum mechanics
• PT-symetrically regularized Eckart,Poeschl-Teller and Hulthen potentials
• PT symmetry breaking and explicit expressions for the pseudo-norm in the Scarf II potential
• Analytic results in the position-dependent mass Schrodinger problem
• Localized modes in ${\chi }^{(2)}$ media with $\PT$-symmetric localized potential
• Solitons and their stability in the nonlocal nonlinear Schroedinger equation with PT-symmetric potentials
• On stable solitons and interactions of the generalized Gross-Pitaevskii equation with PT-and non-PT-symmetric potentials
• Quasi-exactly solvable quartic potentials with centrifugal and Coulombic terms
• Conditional observability
• A PT Symmetric QES Partner to the Khare Mandal Potential With Real Eigen Values
• Relativistic supersymmetric quantum mechanics based on Klein-Gordon equation
• A note on the integrability of non-Hermitian extensions of Calogero-Moser-Sutherland models
• An exactly solvable PT symmetric potential from the Natanzon class
• Isospectral partners for a complex PT-invariant potential
• The structure of supersymmetry in $\mathcal{P}\mathcal{T}$ symmetric quantum mechanics
• Solvable simulation of a double-well problem in PT symmetric quantum mechanics
• Matching method and exact solvability of discrete PT-symmetric square wells
• Self-isospectral tri-supersymmetry in PT-symmetric quantum systems with pure imaginary periodicity
• Real spectra for non-Hermitian Dirac equation in 1+1 dimensions with a most general coupling
• PT - symmetrized supersymmetric quantum mechanics
• Anomalous doublets of states in a PT symmetric quantum model
• PT-symmetric supersymmetry in a solvable short-range model
• A new solvable complex PT-symmetric potential
• Accidental crossings of eigenvalues in one-dimensional complex PT-symmetric Scarf-II potential
• Poeschl-Teller paradoxes
• Solvable PT symmetric Hamiltonians