A semi-classical treatment of the coupled channel equation with non-local interaction, (1)

Coupled channel problem in one spatial dimension with non-local potentials of general type is treated by the WKB method. This is done by generalizing the WKB treatment of the single channel problem with non-local potentials proposed before and applied with great success to the interactions of the resonating group method. Properties of the obtained WKB wave function are studied in detail and the conservation of the flux is investigated. Characters and roles of two kinds of turning points are studied in detail by comparing with the coupled channel problem with local potentials. (author)