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.
Citation:
V. V. Kucherenko, “Quasiclassical asymptotics of a point-source function for the stationary Schrödinger equation”, TMF, 1:3 (1969), 384–406; Theoret. and Math. Phys., 1:3 (1969), 294–310
\Bibitem{Kuc69}
\by V.~V.~Kucherenko
\paper Quasiclassical asymptotics of a~point-source function for the stationary Schr\"odinger equation
\jour TMF
\yr 1969
\vol 1
\issue 3
\pages 384--406
\mathnet{http://mi.mathnet.ru/tmf4587}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=479166}
\transl
\jour Theoret. and Math. Phys.
\yr 1969
\vol 1
\issue 3
\pages 294--310
\crossref{https://doi.org/10.1007/BF01035745}
Linking options:
https://www.mathnet.ru/eng/tmf4587
https://www.mathnet.ru/eng/tmf/v1/i3/p384
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