Abstract: The spin of an electron is a pure quantum property without the counterpart of the classical physics. Its basic property is that the value of the spin in any direction in the spin space is. Finding a visual example to demonstrate this property of the electron spin is the key and difficult point in quantum mechanics teaching. In this work, the similarity transformation is used to rotate  to  which represents an arbitrary direction in the spin space by constructing three different rotation operators, and then the eigenvalue of the spin S^n is verified to be . Additionally, this paper shows the advantages and disadvantages of the three rotation operators in verifying the basic properties of the spin.

Key words: spin, rotation operator, group SO(3), group SU(2), similarity transformation