In [Phys. Rev. A 90, 023833 (2014)], we offer a solution to the problem of constructing a scattering potential v(x) which possesses scattering properties of one's choice at an arbitrarily prescribed wave number. This solution involves expressing v(x) as the sum of n <= 6 finite-range unidirectionally invisible potentials. We improve this result by reducing the upper bound on n from 6 to 4. In particular, we show that we can construct v(x) as the sum of up to n = 3 finite-range unidirectionally invisible potentials, unless if it is required to be bidirectionally reflectionless.
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机译：在[Phys。 Rev. A 90，023833（2014）]中，我们提供了一个解决方案，以构造具有任意选择波数的，具有选择散射特性的散射势v（x）。此解决方案涉及将v（x）表示为n <= 6有限范围单向不可见电势的总和。我们通过将n的上限从6减小到4来改善此结果。特别是，我们证明了可以构造v（x）作为n = 3有限范围单向不可见势的总和，除非需要是双向无反射的。
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