Systematic construction of non-autonomous Hamiltonian equations of Painlev\'e-type. III. Quantization
Exactly Solvable and Integrable Systems
2022-05-17 v1 Mathematical Physics
math.MP
Quantum Physics
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.
Keywords
Cite
@article{arxiv.2205.07327,
title = {Systematic construction of non-autonomous Hamiltonian equations of Painlev\'e-type. III. Quantization},
author = {Maciej Błaszak and Krzysztof Marciniak},
journal= {arXiv preprint arXiv:2205.07327},
year = {2022}
}