ISOMONODROMIC QUANTIZATION OF THE SECOND PAINLEVE EQUATION BY MEANS OF CONSERVATIVE HAMILTONIAN SYSTEMS WITH TWO DEGREES OF FREEDOM

For the three nonstationary Schrodinger equations ih Psi(tau) = H(x,y,-i (h) over bar partial derivative/partial derivative x,-ih partial derivative/partial derivative y)Psi, solutions are constructed that correspond to conservative Hamiltonian systems with two degrees of freedom whose general solutions can be represented by those of the second Painleve equation. These solutions of the Schrodinger equations are expressed via fundamental solutions of systems of linear equations arising in the isomonodromic deformations method, the compatibility condition of which is the second Painleve equation. The constructed solutions of two nonstationary Schrodinger equations are globally smooth. Some of the smooth solutions in question of one of these two equations exponentially tend to zero as x(2) + y(2) -> infinity if the corresponding solutions of linear systems that are used in the method of isomonodromic deformations are compatible on the so-called 1-tronquee solutions of the second Painleve equation.