Quasiclassical asymptotics of a point-source function for the stationary Schrödinger equation

Formulas for the quasiclassical asymptotics of point-source (Green's) functions (uniform with respect to $x$) of the stationary Schrödinger equation are derived. Assuming that the system of Newton's equations in the potential field $V(x)$, where $V(x)$ is a smooth and rapidly diminishing function, has no finite orbits at the energy level $E$, a proof of the quasiclassical asymptotics for the point-source function is presented.