Complex SUSY Transformations and the Painlevé IV Equation

[摘要] In this paper we will explicitly work out the complex first-order SUSY transformation for the harmonic oscillator in order to obtain both real and complex new exactly-solvable potentials. Furthermore, we will show that this systems lead us to exact complex solutions of the Painlevé IV equation with complex parameters. We present some concrete examples of such solutions.

[关键词] supersymmetric quantum mechanics;Painlev´e equations;dif ferential equations;quantum harmonic oscillator;polynomial Heisenberg algebras