Abstract
The relationship between the Heun class of second-order linear equations and the Painlevé second-order nonlinear equations is studied. The symbol of the Heun class equations is regarded as a quantum Hamiltonian. The independent variable and the differentiation operator correspond to the canonical variables and one of the parameters of the equation is assumed to be time. Painlevé equations appear to be Euler - Lagrange equations related to corresponding classical motion.