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

V. V. Kucherenko


Abstract: 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.

Received: 23.04.1969

 English version: Theoretical and Mathematical Physics, 1969, 1:3, 294–310

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