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Stationary Flows of the Parabolic Potential Barrier in Two Dimensions

Toshiki Shimbori·Tsunehiro Kobayashi
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Abstract

In the two-dimensional isotropic parabolic potential barrier $V(x, y)=V_0 -mγ^2 (x^2+y^2)/2$, 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 $W=\pmγz^2/2$.

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Toshiki Shimbori, Tsunehiro Kobayashi. 2000-06-05. Stationary Flows of the Parabolic Potential Barrier in Two Dimensions. https://doi.org/10.1088/0305-4470%2F33%2F42%2F311

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