Stationary Flows of the Parabolic Potential Barrier in Two Dimensions

Details Stationary Flows of the Parabolic Potential Barrier in Two Dimensions Stationary Flows of the Parabolic Potential Barrier in Two Dimensions

2000-06-05

arxiv.org/abs/quant-ph/0006019v1

Physics

Quantum Physics

12 pages, AmS-LaTeX, 4 figures

Scientific paper

10.1088/0305-4470/33/42/311

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 that are expressed by the complex velocity potentials $W=\pm\gamma z^2/2$.

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