Complex Calogero model with real energies

Abstract

We show that and how PT symmetry (interpreted as a "weakened Hermiticity") can be extended to the exactly solvable two- and three-particle Calogero model.

16 pages, 3 figures, submitted to J. Phys. A

References in corpus (10)

• PT -symmetric harmonic oscillators
• Supersymmetry without hermiticity
• A new PT symmetric complex Hamiltonian with a real spectra
• Some properties of eigenvalues and eigenfunctions of the cubic oscillator with imaginary coupling constant
• Conjecture on the Interlacing of Zeros in Complex Sturm-Liouville Problems
• Variational Ansatz for PT-Symmetric Quantum Mechanics
• The Coulomb - harmonic oscillator correspondence in PT-symmetric quantum mechanics
• Complex Square Well --- A New Exactly Solvable Quantum Mechanical Model
• PT-symetrically regularized Eckart,Poeschl-Teller and Hulthen potentials
• Quasi-exactly solvable quartic potentials with centrifugal and Coulombic terms

Cited by in corpus (50)

• Pseudo-Hermiticity versus PT Symmetry: The necessary condition for the reality of the spectrum of a non-Hermitian Hamiltonian
• Pseudo-Hermiticity versus PT-Symmetry II: A complete characterizatio n of non-Hermitian Hamiltonians with a real spectrum
• Pseudo-Hermiticity versus PT-Symmetry III: Equivalence of pseudo-Her miticity and the presence of antilinear symmetries
• The ODE/IM Correspondence
• Pseudo-Supersymmetric Quantum Mechanics and Isospectral Pseudo-Hermi tian Hamiltonians
• Bound states of the Dirac equation for the PT-symmetric generalized Hulthen potential by the Nikiforov-Uvarov method
• Spontaneous breakdown of PT symmetry in the solvable square-well model
• Non-Hermitian supersymmetry and singular PT symmetrized oscillators
• $PT$-symmetric invisible defects and confluent Darboux-Crum transformations
• Complex Optical Potentials and Pseudo-Hermitian Hamiltonians
• Exponential Type Complex and non-Hermitian Potentials in PT-Symmetric Quantum Mechanics
• Construction of a unique metric in quasi-Hermitian quantum mechanics: non-existence of the charge operator in a 2 x 2 matrix model
• PT-symmetric deformations of integrable models
• PT symmetric pseudo-perturbation recipe; an imaginary cubic oscillator with spikes
• Coupled-channel version of PT-symmetric square well
• On the Real Spectra of Calogero Model with Complex Coupling
• A note on the integrability of non-Hermitian extensions of Calogero-Moser-Sutherland models
• Solvable simulation of a double-well problem in PT symmetric quantum mechanics
• Perfectly invisible $\mathcal{P}\mathcal{T}$-symmetric zero-gap systems, conformal field theoretical kinks, and exotic nonlinear supersymmetry
• Twisted kinks, Dirac transparent systems and Darboux transformations
• PT-symmetric deformations of Calogero models
• Should PT symmetric quantum mechanics be interpreted as nonlinear?
• Antilinear deformations of Coxeter groups, an application to Calogero models
• PT symmetric models in more dimensions and solvable square-well versions of their angular Schroedinger equations
• Hidden symmetries of rationally deformed superconformal mechanics
• From real fields to complex Calogero particles
• Trigonometric identities, angular Schrödinger equations and a new family of solvable models
• Anomalous doublets of states in a PT symmetric quantum model
• On the Role of the Normalization Factors ${\kappa }_n$ and of the Pseudo-Metric $\mathcal{P}\ne {\mathcal{P}}^{†}$ in Crypto-Hermitian Quantum Models
• Comment on "Supersymmetry and Singular Potentials" by Das and Pernice [Nucl. Phys. B 561 (1999) 357]
• PT-symmetric extensions of the supersymmetric Korteweg-de Vries equation
• Non-Hermitian multi-particle systems from complex root spaces
• Exactly Solvable Three-body SUSY Systems with Internal Degrees of Freedom
• A class of exactly solvable rationally extended Calogero-Wolfes type 3-body problems
• Poeschl-Teller paradoxes
• Constructing Exactly Solvable Pseudo-hermitian Many-particle Quantum Systems by Isospectral Deformation
• Anomalous real spectra of non-Hermitian quantum graphs in strong-coupling regime
• Exactly solvable three-body Calogero-type model with translucent two-body barriers
• Integrable models from PT-symmetric deformations
• Deconstructing non-Dirac-hermitian supersymmetric quantum systems
• Supersymmetric Many-particle Quantum Systems with Inverse-square Interactions
• Solvable PT symmetric Hamiltonians
• Applications of the potential algebras of the two-dimensional Dirac-like operators
• $\eta$-weak-pseudo-Hermiticity generators and radially symmetric Hamiltonians
• PT invariant complex E(8) root spaces
• Exact wave functions and entropies of the one dimensional Regularized Calogero model
• Planarizable Supersymmetric Quantum Toboggans
• Algebraic integrability of $\mathcal{P}\mathcal{T}$-deformed Calogero models
• Calogero-like model without rearrangement symmetry
• Non-Hermitian superintegrable systems