This article uses the supersymmetric WKB approximation to obtain the approximate energy levels and wave functions of the anharmonic potential V（r） = ar^2 ＋ br^-4 ＋ cr^-6 in order to tesify the correctness between ...This article uses the supersymmetric WKB approximation to obtain the approximate energy levels and wave functions of the anharmonic potential V（r） = ar^2 ＋ br^-4 ＋ cr^-6 in order to tesify the correctness between [Phys. Left. A 170 （1992） 335] and the paper written by M. Landtman [Phys. Left. A 175 （1993） 147].展开更多
Asymptotic eigenvalues and eigenfunctions for the Orr-Sommerfeld equation in two-dimensional and three-dimensional incompressible flows on an infinite domain and on a semi-infinite domain are obtained. Two configurati...Asymptotic eigenvalues and eigenfunctions for the Orr-Sommerfeld equation in two-dimensional and three-dimensional incompressible flows on an infinite domain and on a semi-infinite domain are obtained. Two configurations are considered, one in which a short-wave limit approximation is used, and another in which a long-wave limit approximation is used. In the short-wave limit, Wentzel-Kramers-Brillouin (WKB) methods are utilized to estimate the eigenvalues, and the eigenfunctions are approximated in terms of Green’s functions. The procedure consists of transforming the Orr-Sommerfeld equation into a system of two second order ordinary differential equations for which the eigenvalues and the eigenfunctions can be approximated. In the long-wave limit approximation, solutions are expressed in terms of generalized hypergeometric functions. Our procedure works regardless of the values of the Reynolds number.展开更多
文摘This article uses the supersymmetric WKB approximation to obtain the approximate energy levels and wave functions of the anharmonic potential V（r） = ar^2 ＋ br^-4 ＋ cr^-6 in order to tesify the correctness between [Phys. Left. A 170 （1992） 335] and the paper written by M. Landtman [Phys. Left. A 175 （1993） 147].
文摘Asymptotic eigenvalues and eigenfunctions for the Orr-Sommerfeld equation in two-dimensional and three-dimensional incompressible flows on an infinite domain and on a semi-infinite domain are obtained. Two configurations are considered, one in which a short-wave limit approximation is used, and another in which a long-wave limit approximation is used. In the short-wave limit, Wentzel-Kramers-Brillouin (WKB) methods are utilized to estimate the eigenvalues, and the eigenfunctions are approximated in terms of Green’s functions. The procedure consists of transforming the Orr-Sommerfeld equation into a system of two second order ordinary differential equations for which the eigenvalues and the eigenfunctions can be approximated. In the long-wave limit approximation, solutions are expressed in terms of generalized hypergeometric functions. Our procedure works regardless of the values of the Reynolds number.
