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TMF, 1984, Volume 61, Number 1, Pages 92–98 (Mi tmf5660)  

Asymptotic solutions of whispering-gallery type for the time-dependent Schrödinger equation

A. A. Denisov


Abstract: Formal asymptotic solutions of the time-dependent Schrödinger equation that are concentrated in the neighborhood of the boundary of a cylindrical region and satisfy the zero-value boundary condition are constructed. It is shown that the leading term in the asymptotic solution can be calculated if the solution is known to the Cauchy problem for the Hamilton system corresponding to the problem of classical mechanics of the motion of a material point subject to a holonomic constraint.

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English version:
Theoretical and Mathematical Physics, 1984, 61:1, 1017–1021

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Received: 20.12.1983

Citation: A. A. Denisov, “Asymptotic solutions of whispering-gallery type for the time-dependent Schrödinger equation”, TMF, 61:1 (1984), 92–98; Theoret. and Math. Phys., 61:1 (1984), 1017–1021

Citation in format AMSBIB
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\by A.~A.~Denisov
\paper Asymptotic solutions of whispering-gallery type for the time-dependent Schr\"{o}dinger equation
\jour TMF
\yr 1984
\vol 61
\issue 1
\pages 92--98
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\mathscinet{http://www.ams.org/mathscinet-getitem?mr=774210}
\zmath{https://zbmath.org/?q=an:0563.35069}
\transl
\jour Theoret. and Math. Phys.
\yr 1984
\vol 61
\issue 1
\pages 1017--1021
\crossref{https://doi.org/10.1007/BF01038550}
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  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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