On eigenfunction approximations for typical non-self-adjoint Schrodinger operators

Efficient approximations are constructed for the eigenfunctions of non-self -adjoint Schrodinger operators in one dimension. The same ideas also apply to the study of resonances of self-adjoint Schrodinger operators which have dilation analytic potentials. In spite of the fact that such eigenfunction s can have surprisingly complicated structures with multiple local maxima, we show that a suitable adaptation of the JWKB method is able to provide ac curate global approximations to them.