Simple applications of fundamental solution method in 1D quantum mechanics A talk given at the conference on: "Geometry Symmetry and Mechanics I" Lisbon, 11-16 July 2001

A method of fundamental solutions has been used to show its effectiveness in solving some well known problems of 1D quantum mechanics (barrier penetrations, over-barrier reflections, resonance states), i.e. those in which we look for exponentially small contributions to semiclassical expansions for considered quantities. Its usefulness for adiabatic transitions in two energy level systems is also mentioned.