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- W4247011990 abstract "This chapter discusses the evaluation of the Green's function for the Schrödinger equation in three dimensions with a smooth potential, in the limit of large quantum numbers. Such an evaluation is possible only after smoothing over the energy, which results in the introduction of complex energies. The zeroth order approximation requires the resolution of the Hamilton–Jacobi equation for complex energies. For a sufficiently large smoothing width, the Green's function is presented in the chapter as a local expansion based on the Taylor series expansion of the potential. Higher order corrections to the semi-classical approximation are derived from an integral equation for the Green's function. The corrections produce the reflected waves from the caustic in particular. The Boltzmann-Krook-Welander method is discussed in the one-dimensional case by considering the limit of a small smoothing width, which yields asymptotic estimates of eigenvalues and eigenfunctions for large quantum numbers, under the assumption that the potential is slowly varying. The chapter presents the quantum corrections to the Thomas-Fermi model, which are derived as a first application." @default.
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- W4247011990 date "1972-01-01" @default.
- W4247011990 modified "2023-09-27" @default.
- W4247011990 title "Asymptotic Evaluation of the Green's Function for Large Quantum Numbers" @default.
- W4247011990 doi "https://doi.org/10.1016/b978-0-12-508201-3.50036-3" @default.
- W4247011990 hasPublicationYear "1972" @default.
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