New possibilities for supersymmetry breakdown in quantum mechanics and second order irreducible Darboux transformations

Abstract

New types of irreducible second order Darboux transformations for the one dimensional Schroedinger equation are described. The main feature of such transformations is that the transformation functions have the eigenvalues grater then the ground state energy of the initial (or reference) Hamiltonian. When such a transformation is presented as a chain of two first order transformations, an intermediate potential is singular and therefore intermediate Hamiltonian can not be Hermitian while the final potential is regular and the final Hamiltonian is Hermitian. Second derivative supersymmetric quantum mechanical model based on a transformation of this kind exhibits properties inherent to models with exact and broken supersymmetry at once.

Cited by in corpus (56)

• Solvable rational extensions of the isotonic oscillator
• N-fold Supersymmetry in Quantum Mechanics - General Formalism -
• Nonlinear Supersymmetry for Spectral Design in Quantum Mechanics
• Intertwining technique for the one-dimensional stationary Dirac equation
• General Forms of a N-fold Supersymmetric Family
• Coherent states for Hamiltonians generated by supersymmetry
• 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
• Second order SUSY transformations with `complex energies'
• Nonlocal supersymmetric deformations of periodic potentials
• Finite-gap systems, tri-supersymmetry and self-isospectrality
• Multistep DBT and regular rational extensions of the isotonic oscillator
• Solvable rational extensions of the Morse and Kepler-Coulomb potentials
• The Phenomenon of Darboux Displacements
• Wronskian formula for confluent second-order supersymmetric quantum mechanics
• SUSY transformations between digonalizable and non-diagonalizable Hamiltonians
• Supersymmetric partners of the trigonometric Poschl-Teller potentials
• Combined state-adding and state-deleting approaches to type III multi-step rationally-extended potentials: applications to ladder operators and superintegrability
• Nonlinear Pseudo-Supersymmetry in the Framework of N-fold Supersymmetry
• A New Family of N-fold Supersymmetry: Type B
• Type A N-fold Supersymmetry and Generalized Bender-Dunne Polynomials
• Phase equivalent chains of Darboux transformations in scattering theory
• sl(2) Construction of Type A N-fold supersymmetry
• Electron in bilayer graphene with magnetic fields leading to shape invariant potentials
• A class of exactly solvable Schroedinger equation with moving boundary conditions
• Bilayer graphene in magnetic fields generated by supersymmetry
• Confluent Chains of DBT: Enlarged Shape Invariance and New Orthogonal Polynomials
• N-fold Supersymmetry in Quantum Mechanics - Analyses of Particular Models -
• Single- and coupled-channel radial inverse scattering with supersymmetric transformations
• Interplay between Riccati, Ermakov and Schroedinger equations to produce complex-valued potentials with real energy spectrum
• Quantum mechanical spectral engineering by scaling intertwining
• Non linear pseudo-bosons versus hidden Hermiticity. II: The case of unbounded operators
• Two-Dimensional Supersymmetry: From SUSY Quantum Mechanics to Integrable Classical Models
• Supersymmetric partners of the harmonic oscillator with an infinite potential barrier
• Irreducible second order SUSY transformations between real and complex potentials
• Classification of Type A N-fold supersymmetry
• SUSY partners of the truncated oscillator, Painlevé transcendents and Bäcklund transformations
• Nonlinear supersymmetry: from classical to quantum mechanics
• Exact propagators for SUSY partners
• Coherent states for the supersymmetric partners of the truncated oscillator
• Darboux transformations for quasi-exactly solvable Hamiltonians
• Spectral Design for Matrix Hamiltonians: Different Methods of Constructing of a Matrix Intertwining Operator
• Polynomial Supersymmetry for Matrix Hamiltonians
• Minimal Realizations of Supersymmetry for Matrix Hamiltonians
• Ladder operators and coherent states for multi-step supersymmetric rational extensions of the truncated oscillator
• Factorization of non-linear supersymmetry in one-dimensional Quantum Mechanics. II: proofs of theorems on reducibility
• Supersymmetrization of the Franke-Gorini-Kossakowski-Lindblad-Sudarshan equation
• New Implicitly Solvable Potential Produced by Second Order Shape Invariance
• Higher Order Supersymmetric Truncated Oscillators
• Double complex SUSY-transformations: deformations of real potentials and their spectral characteristics
• An affine Weyl group characterization of polynomial Heisenberg algebras
• Polynomial supersymmetry for matrix Hamiltonians: proofs
• Search of a general form of superpotential in hierarchy with discrete energy spectrum
• Higher order intertwining approach to quasinormal modes
• Perfect Quantum State Revivals: Designing Arbitrary Potentials with Specified Energy Levels