Non-Hermitian supersymmetry and singular PT symmetrized oscillators

Abstract

SUSY partnership between singular potentials often breaks down. Via regularization it can be restored on certain ad hoc subspaces of Hilbert space [Das and Pernice, Nucl. Phys. B 561 (1999) 357]. Within the naturally complexified (so called PT symmetric) quantum mechanics we show how SUSY between strongly singular harmonic oscillators can completely be re-established. Our recipe leads to a new form of the bosonic creation and annihilation operators and proves continuous near the usual regular (i.e., linear harmonic) limit.

24 pages incl. 5 tables and 1 figure

References in corpus (10)

• 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
• Supersymmetry and the spontaneous breakdown of PT symmetry
• Space of State Vectors in PT Symmetrical Quantum Mechanics
• A PT Symmetric QES Partner to the Khare Mandal Potential With Real Eigen Values
• The Interpretation of Quantum-Mechanical Models with Non-Hermitian Hamiltonians and Real Spectra
• Broken Supersymmetric Shape Invariant Systems and Their Potential Algebras
• Poeschl-Teller paradoxes
• Exactly solvable three-body Calogero-type model with translucent two-body barriers
• Annihilation and creation operators in non-Hermitian supersymmetric quantum mechanics

Cited by in corpus (29)

• Scattering theory using smeared non-Hermitian potentials
• A return to observability near exceptional points in a schematic PT-symmetric model
• Conditional observability
• Solvability and PT-symmetry in a double-well model with point interactions
• Relativistic supersymmetric quantum mechanics based on Klein-Gordon equation
• Asymptotic solvability of an imaginary cubic oscillator with spikes
• An exactly solvable PT symmetric potential from the Natanzon class
• Isospectral partners for a complex PT-invariant potential
• Crypto-unitary forms of quantum evolution operators
• Pseudo-bosons, so far
• Construction of PT-asymmetric non-Hermitian Hamiltonians with CPT-symmetry
• Pseudo supersymmetric partners for the generalized Swanson model
• Quantum phase transitions in nonhermitian harmonic oscillator
• Non linear pseudo-bosons versus hidden Hermiticity. II: The case of unbounded operators
• Comment on "Supersymmetry and Singular Potentials" by Das and Pernice [Nucl. Phys. B 561 (1999) 357]
• PT-symmetric supersymmetry in a solvable short-range model
• Quantum star-graph analogues of PT-symmetric square wells
• Supersymmetric model of a Bose-Einstein condensate in a $\mathcal{P}\mathcal{T}$-symmetric double-delta trap
• Determination of the domain of the admissible matrix elements in the four-dimensional PT-symmetric anharmonic model
• PT-symmetric regularizations in supersymmetric quantum mechanics
• Anomalous real spectra of non-Hermitian quantum graphs in strong-coupling regime
• New Exactly Solvable Isospectral Partners for PT Symmetric Potentials
• Exact Solutions of the Schrödinger Equation with position-dependent effective mass via general point canonical transformation
• $\mathcal{P}\mathcal{T}$ symmetric models with nonlinear pseudo supersymmetry
• Exploring Branched Hamiltonians for a Class of Nonlinear Systems
• Quantum knots
• Hermitian - non-Hermitian interfaces in quantum theory
• Planarizable Supersymmetric Quantum Toboggans
• $\mathcal{P}\mathcal{T}$-like phase transitions from square roots of supersymmetric Hamiltonians