前言：

In linear algebra, we know that the two similar matrices can be connected by a similar transformation. Similarly, in quantum mechanics, similar transformation of an observable quantity (operator) can also obtain some results we want. Many similar transformations, such as the translation of time and space, are often realized by power exponent. In these cases, Baker-Hausdorff formula can be used in the first order. In this article, we will introduce some applications of Baker Hausdorff formula in elementary quantum mechanics. These transformations often appear in the analysis of symmetry and conservation quantity.