Asymptotical expansions for ground states of Schrodinger equation

The method of calculation of asymptotical expansions for ground state of Schrodinger equation in case of smooth potentials is proposed. These asymptotical expansions are solutions of the corresponding eigenvalue tasks in quadratures. Unlike quasiclassical approach of WKB the proposed solutions are applicable for the ground states and allow to find a logarithmic derivative of wave function in a whole area of its definition. For some simplest potentials the calculated asymptotical expansions converge to exact solution.