We construct a smooth realistic barrier potential that can generate resonances above the top of the barrier provided a parameter λ controlling the flatness of the barrier is larger than the critical value λ = √ 2. The energies and widths of resonances are expressed analytically in terms of the characteristics of the barrier, namely height, range and flatness. In order to obtain a more versatile and asymmetric barrier, two symmetric barriers are merged together side by side and the exact transmission coefficient across such a barrier is derived.
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