标题： 非自治哈密顿方程的系统构造 III. 量子化 显示英文标题

标题： Systematic construction of non-autonomous Hamiltonian equations of Painlevé-type. III. Quantization

摘要： 这是我们在探索Stäckel型动力系统与Painlevé型动力系统之间联系的文章系列中的第三篇。在本文中，我们提出了一种方法，将第一部分中最小量化准Stäckel哈密顿量变形为满足量子Frobenius条件的自伴算子，从而保证相应的薛定谔方程具有共同的多时间解。 正如经典情况一样，我们在这里得到了磁性和非磁性系统的族。我们还展示了这两类量子系统之间存在依赖于多时间的量子规范映射。 显示英文摘要

摘要： This is the third article in our series of articles exploring connections between dynamical systems of St\"ackel-type and of Painlev\'e-type. In this article we present a method of deforming of minimally quantized quasi-St\"ackel Hamiltonians, considered in Part I to self-adjoint operators satisfying the quantum Frobenius condition, thus guaranteeing that the corresponding Schr\"odinger equations posses common, multi-time solutions. As in the classical case, we obtain here both magnetic and non-magnetic families of systems. We also show the existence of multitime-dependent quantum canonical maps between both classes of quantum systems.