Abstract
Supersymmetry transformations are used to generate exactly solvable potentials departing from the complex oscillator. The corresponding Hamiltonians are shown to be ruled by polynomial Heisenberg algebras. A process for reducing the degree of these algebras to 2 is used to connect such systems with the Painlevé IV equation, thus leading to a simple algorithm for generating Painlevé IV transcendents.
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Fernández, D.J. (2021). Painlevé IV Transcendents Generated from the Complex Oscillator. In: Paranjape, M.B., MacKenzie, R., Thomova, Z., Winternitz, P., Witczak-Krempa, W. (eds) Quantum Theory and Symmetries. CRM Series in Mathematical Physics. Springer, Cham. https://doi.org/10.1007/978-3-030-55777-5_4
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DOI: https://doi.org/10.1007/978-3-030-55777-5_4
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