Dariusz Chruscinski
Quantum Mechanics of Damped Systems II. Damping and 
Parabolic Potential Barrier.
(224K, Postscript)

ABSTRACT.  We investigate the resonant states for the parabolic potential 
barrier known also as inverted or reversed oscillator. They 
correspond to the poles of meromorphic continuation of the 
resolvent operator to the complex energy plane. As a byproduct we 
establish an interesting relation between parabolic cylinder 
functions (representing energy eigenfunctions of our system) and a 
class of Gel'fand distributions used in our recent paper.