In this paper, it is considered to find a way for defining non-commutative spaces by ordinary commutative ones and vice versa. A novel parameter which has not been considered so far is represented. This parameter describes equivalent spaces. Also, we searched concepts of these new parameters with one problem. Non-commutativity in total space is important here because it could explain more concepts. As we knew SW method (Seiberg–Witten) explained non-commutativity so here, we showed that it was not suitable for some conditions in the end, we considered Hamiltonian of free particle in new non-commutativity, and we found concepts of new parameters.

中文翻译：

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量子力学中非交换性的新参数

在本文中，考虑找到一种通过普通可交换空间来定义非可交换空间的方法，反之亦然。表示了迄今为止尚未考虑的新颖参数。此参数描述等效空间。此外，我们搜索这些新参数的概念时遇到了一个问题。总空间的不可交换性在这里很重要，因为它可以解释更多的概念。众所周知，SW方法（Seiberg–Witten）解释了非交换性，因此在这里，我们证明它最终不适用于某些条件，我们在新的非交换性中考虑了自由粒子的哈密顿量，并发现了新参数的概念。