Second order SUSY transformations with `complex energies'

Abstract

Second order supersymmetry transformations which involve a pair of complex conjugate factorization energies and lead to real non-singular potentials are analyzed. The generation of complex potentials with real spectra is also studied. The theory is applied to the free particle, one-soliton well and one-dimensional harmonic oscillator.

11 pages, 2 figures, submitted on 23 August 2002 to Phys. Lett. A

References in corpus (23)

• Real Spectra in Non-Hermitian Hamiltonians Having PT Symmetry
• 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
• Schrödinger operators with complex potential but real spectrum
• Higher-Derivative Supersymmetry and the Witten Index
• SUSY Quantum Mechanics with Complex Superpotentials and Real Energy Spectra
• Second Order Derivative Supersymmetry and Scattering Problem
• A family of complex potentials with real spectrum
• Polynomial SUSY in Quantum Mechanics and Second Derivative Darboux Transformation
• The finite difference algorithm for higher order supersymmetry
• New possibilities for supersymmetry breakdown in quantum mechanics and second order irreducible Darboux transformations
• SUSUSY quantum mechanics
• The supersymmetric modified Poschl-Teller and delta-well potentials
• Generating Complex Potentials with Real Eigenvalues in Supersymmetric Quantum Mechanics
• Group theoretical approach to the intertwined Hamiltonians
• Riccati equation, Factorization Method and Shape Invariance
• Exactly Solvable Hydrogen-like Potentials and Factorization Method
• Nonlocal supersymmetric deformations of periodic potentials
• Complexified PSUSY and SSUSY interpretations of some PT-symmetric Hamiltonians possessing two series of real energy eigenvalues
• The Phenomenon of Darboux Displacements
• New Families of Isospectral Hydrogen-like potentials
• The partnership of potentials in Quantum Mechanics and Shape Invariance

Cited by in corpus (34)

• Nonlinear Supersymmetry for Spectral Design in Quantum Mechanics
• Nonlinear Supersymmetric Quantum Mechanics: concepts and realizations
• The confluent algorithm in second order supersymmetric quantum mechanics
• Extended Krein-Adler theorem for the translationally shape invariant potentials
• Multistep DBT and regular rational extensions of the isotonic oscillator
• New supersymmetry-generated complex potentials with real spectra
• Wronskian formula for confluent second-order supersymmetric quantum mechanics
• Factorization method and new potentials from the inverted oscillator
• Supersymmetric partners of the trigonometric Poschl-Teller potentials
• Trends in supersymmetric quantum mechanics
• Generalized coherent states for time-dependent and nonlinear Hamiltonians via complex Riccati equations
• Non-Hermitian SUSY Hydrogen-like Hamiltonians with real spectra
• Nonlinear Pseudo-Supersymmetry in the Framework of N-fold Supersymmetry
• Gamow-Siegert functions and Darboux-deformed short range potentials
• Single- and coupled-channel radial inverse scattering with supersymmetric transformations
• Optical potentials using resonance states in Supersymmetric Quantum Mechanics
• Complex SUSY Transformations and the Painlevé IV Equation
• Solutions to the Painlevé V equation through supersymmetric quantum mechanics
• Complex oscillator and Painlevé IV equation
• Nonlinear supersymmetry: from classical to quantum mechanics
• Quadratic pseudosupersymmetry in two-level systems
• Rectangular Potentials in a Semi-Harmonic Background: Spectrum, Resonances and Dwell Time
• New Exactly Solvable Isospectral Partners for PT Symmetric Potentials
• Gamow vectors and Supersymmetric Quantum Mechanics
• Polynomial Supersymmetry for Matrix Hamiltonians
• Spectral Design for Matrix Hamiltonians: Different Methods of Constructing of a Matrix Intertwining Operator
• $\mathcal{P}\mathcal{T}$ symmetric models with nonlinear pseudo supersymmetry
• Minimal Realizations of Supersymmetry for Matrix Hamiltonians
• Complex Supersymmetry in Graphene
• Factorization of non-linear supersymmetry in one-dimensional Quantum Mechanics. II: proofs of theorems on reducibility
• Extended WKB method, resonances and supersymmetric radial barriers
• Supersymmetry Transformations for Delta Potentials
• Beyond conventional factorization: Non-Hermitian Hamiltonians with radial oscillator spectrum
• Polynomial supersymmetry for matrix Hamiltonians: proofs