Shimbori, Toshiki; Kobayashi, Tsunehiro Stationary flows of the parabolic potential barrier in two dimensions. (English) Zbl 1066.81536 J. Phys. A, Math. Gen. 33, No. 42, 7637-7652 (2000). Summary: In the two-dimensional isotropic parabolic potential barrier \[ V(x,y) = V_0-m\gamma^2(x^2 + y^2)/2, \] 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 Wikipedia Wolfram MathWorld that are expressed by the complex velocity potentials \(W = \pm\gamma z^2/2\). From the hydrodynamical point of view vortex structures for the general solutions are also studied. Cited in 5 Documents MSC: 81Q05 Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics 35Q05 Euler-Poisson-Darboux equations × Cite Format Result Cite Review PDF Full Text: DOI arXiv