Isomonodromic deformations and “antiquantization” for the simplest ordinary differential equations

We consider three different models of linear differential equations and their isomonodromic deformations. We show that each of the models has its own specificity, although all of them lead to the same final result. It turns out that isomonodromic deformations are closely related to the Hamiltonian structure of both classical mechanics and quantum mechanics. __________ Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 150, No. 1, pp. 143–151, January, 2007.