Thomas–Fermi model is considered here to make it cogent to capture the Planck-scale effect with the use of a generalization of uncertainty relation. Here generalization contains both linear and quadratic terms of momentum. We first reformulate the Thomas–Fermi model for the non-relativistic case. We have shown that it can also be reformulated for taking into account the relativistic effect. We study the dialectic screening for both the non-relativistic and relativistic cases and find out the Fermi length for both the cases explicitly.

中文翻译：

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关于重新制定 Thomas-Fermi 模型以使其与普朗克尺度兼容

此处考虑了 Thomas-Fermi 模型，以便通过使用不确定性关系的概括来捕捉普朗克尺度效应。这里泛化包含动量的线性和二次项。我们首先为非相对论情况重新制定 Thomas-Fermi 模型。我们已经表明，它也可以重新制定以考虑相对论效应。我们研究了非相对论和相对论情况的辩证筛选，并明确地找出了这两种情况的费米长度。