Related papers: Systematic construction of non-autonomous Hamiltonian equations of Painlev\'e-type. III. Quantization

Systematic construction of non-autonomous Hamiltonian equations of Painlev\'e-type. III. Quantization

URL: http://arxiv.org/abs/2205.07327v1
Date: Sun, 15 May 2022 16:35:56 GMT
Title: Systematic construction of non-autonomous Hamiltonian equations of Painlev\'e-type. III. Quantization
Authors: Maciej B{\l}aszak and Krzysztof Marciniak
Abstract summary: This is the third article in our series of articles exploring connections between dynamical systems of St"ackel-type and Painlev'e-type.
Score: 0.0
License: http://creativecommons.org/licenses/by/4.0/
Abstract: 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.

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