On the general family of third-order shape-invariant Hamiltonians related to generalized Hermite polynomials
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Publication:2104195
DOI10.1016/j.physd.2022.133529OpenAlexW4296887176MaRDI QIDQ2104195
Publication date: 9 December 2022
Published in: Physica D (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/2203.05631
orthogonal polynomialsfourth Painlevé equationgeneralized Hermite polynomialsrational potentialsshape-invariant Hamiltonian
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Cites Work
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- Oscillation theorems for the Wronskian of an arbitrary sequence of eigenfunctions of Schrödinger's equation
- Zeros of exceptional Hermite polynomials
- Supersymmetric quantum mechanics and Painlevé IV equation
- Factorization method in quantum mechanics
- Special polynomials associated with rational solutions of the Painlevé equations and applications to soliton equations
- Studies on the Painlevé equations. III: Second and fourth Painlevé equations, \(P_{II}\) and \(P_{IV}\)
- Dressing chains and the spectral theory of the Schrödinger operator
- Recuttings of polygons
- Systems with higher-order shape invariance: spectral and algebraic properties
- Bi-orthogonal approach to non-Hermitian Hamiltonians with the oscillator spectrum: generalized coherent states for nonlinear algebras
- Painlevé differential equations in the complex plane
- A modification of Crum's method
- Darboux transformation, factorization, and supersymmetry in one-dimensional quantum mechanics
- Zeros of Wronskians of Hermite polynomials and Young diagrams
- Cyclic shape invariant potentials.
- Complete classification of rational solutions of \(A_{2n}\)-Painlevé systems
- Spectral theory of exceptional Hermite polynomials
- Quantum theory from a nonlinear perspective. Riccati equations in fundamental physics
- On certain determinants whose elements are orthogonal polynomials
- SECOND ORDER DERIVATIVE SUPERSYMMETRY, q DEFORMATIONS AND THE SCATTERING PROBLEM
- Connection between quantum systems involving the fourth Painlevé transcendent and k-step rational extensions of the harmonic oscillator related to Hermite exceptional orthogonal polynomial
- Solutions to the Painlevé V equation through supersymmetric quantum mechanics
- Factorization method and new potentials with the oscillator spectrum
- Superintegrability with third order integrals of motion, cubic algebras, and supersymmetric quantum mechanics. II. Painlevé transcendent potentials
- Exceptional Laguerre and Jacobi polynomials and the corresponding potentials through Darboux–Crum transformations
- Superintegrability with third order integrals of motion, cubic algebras, and supersymmetric quantum mechanics. I. Rational function potentials
- Factorization: little or great algorithm?
- The fourth Painlevé equation and associated special polynomials
- Bäcklund Transformations and Solution Hierarchies for the Fourth Painlevé Equation
- Higher-order SUSY, linearized nonlinear Heisenberg algebras and coherent states
- Third-order ladder operators, generalized Okamoto and exceptional orthogonal polynomials
- Higher order recurrence relation for exceptional Charlier, Meixner, Hermite and Laguerre orthogonal polynomials
- Infinitely many shape-invariant potentials and cubic identities of the Laguerre and Jacobi polynomials
- Coherent states for Hamiltonians generated by supersymmetry
- Rational extensions of the quantum harmonic oscillator and exceptional Hermite polynomials
- Recurrence relations of the multi-indexed orthogonal polynomials
- The Factorization Method
- ASSOCIATED STURM-LIOUVILLE SYSTEMS
- Fourth Painlevé and Ermakov equations: quantum invariants and new exactly-solvable time-dependent Hamiltonians
- Recurrence relations for exceptional Hermite polynomials
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