Two families of superintegrable and isospectral potentials in two dimensions
arXiv:quant-ph/0201099 · doi:10.1063/1.1463217
Abstract
As an extension of the intertwining operator idea, an algebraic method which provides a link between supersymmetric quantum mechanics and quantum (super)integrability is introduced. By realization of the method in two dimensions, two infinite families of superintegrable and isospectral stationary potentials are generated. The method makes it possible to perform Darboux transformations in such a way that, in addition to the isospectral property, they acquire the superintegrability preserving property. Symmetry generators are second and fourth order in derivatives and all potentials are isospectral with one of the Smorodinsky-Winternitz potentials. Explicit expressions of the potentials, their dynamical symmetry generators and the algebra they obey as well as their degenerate spectra and corresponding normalizable states are presented.
22 pages, only four typos are corrected
References in corpus (9)
- Supersymmetry and Quantum Mechanics
- Quadratic Poisson algebras for two dimensional classical superintegrable systems and quadratic associative algebras for quantum superintegrable systems
- Path Integral Discussion for Smorodinsky-Winternitz Potentials: I.\ Two- and Three Dimensional Euclidean Space
- Exact Solvability of Superintegrable Systems
- Polynomial SUSY in Quantum Mechanics and Second Derivative Darboux Transformation
- Intertwined isospectral potentials in an arbitrary dimension
- Integrable Schrödinger operators with magnetic fields: factorisation method on curved surfaces
- Intertwining relations of non-stationary Schrödinger operators
- On form-preserving transformations for the time-dependent Schrödinger equation
Cited by in corpus (49)
- Nonlinear Supersymmetric Quantum Mechanics: concepts and realizations
- Bloch-like waves in random-walk potentials based on supersymmetry
- Examples of Pseudo-bosons in quantum mechanics
- Intertwined Hamiltonians in Two Dimensional Curved Spaces
- Pseudo-bosons, Riesz bases and coherent states
- Superintegrability and higher order polynomial algebras I
- New families of superintegrable systems from Hermite and Laguerre exceptional orthogonal polynomials
- New ladder operators for a rational extension of the harmonic oscillator and superintegrability of some two-dimensional systems
- Non-Hermitian Hamiltonian for a Modulated Jaynes-Cummings Model with PT Symmetry
- Construction of pseudo-bosons systems
- Non-self-adjoint hamiltonians defined by Riesz bases
- Combined state-adding and state-deleting approaches to type III multi-step rationally-extended potentials: applications to ladder operators and superintegrability
- An infinite family of superintegrable systems from higher order ladder operators and supersymmetry
- More mathematics for pseudo-bosons
- Mathematical aspects of intertwining operators: the role of Riesz bases
- Intertwining operators between different Hilbert spaces: connection with frames
- Pseudo-bosons, so far
- Superintegrable quantum u(3)--systems and higher rank factorizations
- Some results on the dynamics and transition probabilities for non self-adjoint hamiltonians
- Vector coherent states and intertwining operators
- Nonlinear Holomorphic Supersymmetry on Riemann Surfaces
- Intertwining symmetry algebras of quantum superintegrable systems on the hyperboloid
- Intertwining operators for non self-adjoint Hamiltonians and bicoherent states
- Hamiltonians defined by biorthogonal sets
- Supersymmetrical Separation of Variables in Two-Dimensional Quantum Mechanics
- Weak pseudo-bosons
- Generalized Heisenberg algebra and (non linear) pseudo-bosons
- Bi-squeezed states arising from pseudo-bosons
- -symmetric graphene under a magnetic field
- Recurrence approach and higher rank cubic algebras for the -dimensional superintegrable systems
- Two-dimensional superintegrable systems from operator algebras in one dimension
- Appearances of pseudo-bosons from Black-Scholes equation
- A chain of solvable non-Hermitian Hamiltonians constructed by a series of metric operators
- Two-dimensional Schrödinger Hamiltonians with Effective Mass in SUSY Approach
- Non self-adjoint Hamiltonians with complex eigenvalues
- Algebraic calculations for spectrum of superintegrable system from exceptional orthogonal polynomials
- Abstract ladder operators and their applications
- Gibbs states defined by biorthogonal sequences
- Intertwining Symmetry Algebras of Quantum Superintegrable Systems
- Superintegrable systems, polynomial algebra structures and exact derivations of spectra
- Pseudo-fermions in an electronic loss-gain circuit
- Classical and quantum integrability in 3D systems
- Recurrence approach and higher rank polynomial algebras for superintegrable monopole systems
- Dynamical symmetries for superintegrable quantum systems
- Pseudo-Bosons from Landau Levels
- Two-parameters pseudo-bosons
- Extended coupled SUSY, pseudo-bosons and weak squeezed states
- Singular Isotonic Oscillator, Supersymmetry and Superintegrability
- Solution of Second Order Supersymmetrical Intertwining Relations in Minkowski Plane