The one-dimensional parabolic potential barrier dealt with in an earlierpaper is re-examined from the point of view of operator methods, for thepurpose of getting generalized Fock spaces.
In the two-dimensional isotropic parabolic potential barrier V ( x , y ) = V 0 - m γ 2 ( x 2 + y 2 )/2, though it is a model of an unstable system in quantum mechanics, we can obtain the stationary states corresponding to the real energy eigenvalue V 0 . Further, they are infinitely degenerate. For the first few eigenstates, we will find the stationary flows round a right angle that are expressed by the complex velocity potentials W = ±γ z 2 /2. From the hydrodynamical point of view vortex structures for the general solutions are also studied.