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We consider the isomonodromic formulation of the Calogero-Painlev\'emulti-particle systems and proceed to their canonical quantization. We thenproceed to the quantum Hamiltonian reduction on a special representation toradial variables, in analogy with the classical case and also with the theoryof quantum Calogero equations. This quantized version is compared to thegeneralization of a result of Nagoya on integral representations of certainsolutions of the quantum Painlev\'e equations. We also provide multi-particlegeneralizations of these integral representations.

Quantization of Calogero-Painlev\'e System and Multi-Particle Quantum Painlev\'e Equations II-VI