The quasi-classical asymptotic solutions of some problems in mathematical physics

A suitable transformation of the dependent and independent variables in Schrödinger's time-dependent equation for the quantized state of a system of particles in a potential field leades to a linear equation. It is shown by using perturbation theory that this equation has a series solution in powers of $h$ (Planck's constant). In this way it is found to be possible to pass in the limit, as $h\to 0$, from quantum mechanics to classical mechanics. The existence of the total integral of the Hamilton-Jacobi equation is also discussed.