Abstract The formula of refractive index n, which is derived recently from the electromagnetic induction refraction mechanism, contains a parameter V, i.e., the equivalent volume of electron cloud. Dozens of calculated n results by using this formula in previous researches are in good agreement with the measured ones. V determines some properties of materials, such as refractive index and band gap. It is not yet known how to calculate V values of non-spherical electron clouds. In this paper, a calculation method for V values of non-spherical electron clouds is presented as follows: The electron cloud is divided into many little volume elements, and the equivalent volume of each little volume element is calculated with the wave function; V value of the electron cloud is the sum of the equivalent volumes of all its little volume elements. V value of the electron cloud in H2 molecule is obtained in this way. Refractive index of H2 gas is calculated with the V value of H2 molecule, and the calculated refractive index is consistent with the measured datum. In addition to calculating V’s value, the method can also calculate V’s shape. Distribution contour of the equivalent volume of electron cloud in the H2 molecule is like an apple. This work determines the general method of using wave functions to calculate equivalent volume V and refractive index n, is helpful to promote the applications of the formula of refractive index, and provides a means for better understanding the relationship between material properties and their V values.

中文翻译：

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折射率公式中的非球形电子云等效体积V

摘要 近来由电磁感应折射机理推导出的折射率n公式中包含一个参数V，即电子云的等效体积。以往研究中使用该公式计算出的数十个n结果与实测结果吻合较好。V 决定了材料的一些属性，例如折射率和带隙。目前还不知道如何计算非球形电子云的 V 值。本文提出了一种非球面电子云V值的计算方法：将电子云分成许多小体积元，用波函数计算每个小体积元的等效体积；电子云的 V 值是其所有小体积元素的等效体积之和。H2分子中电子云的V值就是这样得到的。H2气体的折射率是用H2分子的V值计算出来的，计算出来的折射率与实测数据一致。除了计算V的值外，该方法还可以计算V的形状。H2分子中等量电子云的分布轮廓就像一个苹果。该工作确定了利用波函数计算等效体积V和折射率n的一般方法，有助于促进折射率公式的应用，为更好地理解材料性质与其V值之间的关系提供了一种手段。计算出的折射率与实测数据一致。除了计算V的值外，该方法还可以计算V的形状。H2分子中等量电子云的分布轮廓就像一个苹果。该工作确定了利用波函数计算等效体积V和折射率n的一般方法，有助于推动折射率公式的应用，为更好地理解材料性质与其V值之间的关系提供了一种手段。计算出的折射率与实测数据一致。除了计算V的值外，该方法还可以计算V的形状。H2分子中等量电子云的分布轮廓就像一个苹果。该工作确定了利用波函数计算等效体积V和折射率n的一般方法，有助于促进折射率公式的应用，为更好地理解材料性质与其V值之间的关系提供了一种手段。