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On the spectral investigation of the scattering problem for some version of one-dimensional Schrödinger equation with turning point

Zaki FA El-Raheem1* and AH Nasser2

Author Affiliations

1 Department of Mathematics, Faculty of Education, Alexandria University, Alexandria, Egypt

2 Department of Mathematics, Faculty of Industrial Education, Helwan University, Cairo, Egypt

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Boundary Value Problems 2014, 2014:97  doi:10.1186/1687-2770-2014-97

Published: 6 May 2014

Abstract

In this paper we introduce and investigate the eigenvalues and the normalizing numbers as well as the scattering function for some version of the one-dimensional Schrödinger equation with turning point on the half line.

MSC: 58C40, 34L25.

Keywords:
initial value problem; the eigenvalues; normalizing numbers; scattering function; asymptotic formula