A. Aslanyan and E. B. Davies
On eigenfunction approximations for typical 
non-self-adjoint Schroedinger operators
(245K, gzipped ps)

ABSTRACT.  We construct efficient approximations for the eigenfunctions 
of non-self-adjoint Schroedinger operators in one dimension. 
The same ideas also apply to the study of resonances of 
self-adjoint Schroedinger operators which have dilation analytic 
potentials. In spite of the fact that such eigenfunctions can have 
surprisingly complicated structures with multiple local maxima, we 
show that a suitable adaptation of the JWKB method is able to provide 
accurate global approximations to them.