论文标题
具有与Painleve VI相关的合理潜力的四阶可促进系统
A fourth-order superintegrable system with a rational potential related to Painleve VI
论文作者
论文摘要
在本文中，我们详细研究了单数谐波振荡器的可整合扩展，其波函数可以用异常的jacobi多项式表示。我们表明，这种哈密顿量承认运动的四阶积分，并使用这种系统的分类来表明潜力提供了与第六个Painlevé方程相关的理性解决方案。此外，我们表明，运动的积分接近形成了立方代数，并描述了该代数的简短变形振荡器表示。
In this paper, we investigate in detail a superintegrable extension of the singular harmonic oscillator whose wave functions can be expressed in terms of exceptional Jacobi polynomials. We show that this Hamiltonian admits a fourth-order integral of motion and use the classification of such systems to show that the potential gives a rational solution associated with the sixth Painlevé equation. Additionally, we show that the integrals of the motion close to form a cubic algebra and describe briefly deformed oscillator representations of this algebra.
