Complex oscillator and Painlevé IV equation
arXiv:1503.08236 · doi:10.1016/j.aop.2015.04.022
Abstract
Supersymmetric quantum mechanics is a powerful tool for generating exactly solvable potentials departing from a given initial one. In this article the first- and second- order supersymmetric transformations will be used to obtain new exactly solvable potentials departing from the complex oscillator. The corresponding Hamiltonians turn out to be ruled by polynomial Heisenberg algebras. By applying a mechanism to reduce to second the order of these algebras, the connection with the Painlevé IV equation is achieved, thus giving place to new solutions for the Painlevé IV equation.
23 pages, 13 figures
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- Connection between quantum systems involving the fourth Painleve transcendent and -step rational extensions of the harmonic oscillator related to Hermite EOP
- On Integrable Ermakov-Painlevé IV Systems
- Dynamical symmetry algebra of two superintegrable two-dimensional systems
- Fourth Painlevé Equation and -Symmetric Hamiltonians