Non-hermitian Hamiltonians and Painlevé IV equation with real parameters
arXiv:1104.3599 · doi:10.1016/j.physleta.2011.06.042
Abstract
In this letter we will use higher-order supersymmetric quantum mechanics to obtain several families of complex solutions of the Painleve IV equation with real parameters. We shall also study the algebraic structure, the eigenfunctions and the energy spectra of the corresponding non-hermitian Hamiltonians.
arXiv comment10 pages, 7 figures
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- Nonlinear Supersymmetric Quantum Mechanics: concepts and realizations
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- Trends in supersymmetric quantum mechanics
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- Supersymmetric partners of the harmonic oscillator with an infinite potential barrier
- Solutions to the Painlevé V equation through supersymmetric quantum mechanics
- SUSY partners of the truncated oscillator, Painlevé transcendents and Bäcklund transformations
- Complex oscillator and Painlevé IV equation
- Complex SUSY Transformations and the Painlevé IV Equation
- Painlevé IV Coherent States
- On Integrable Ermakov-Painlevé IV Systems
- Solution hierarchies for the Painleve IV equation
- Harmonic Oscillator SUSY Partners and Evolution Loops
- Supersymmetric Quantum Mechanics, Engineered Hierarchies of Integrable Potentials, and the Generalised Laguerre Polynomials
- Singular Isotonic Oscillator, Supersymmetry and Superintegrability