Abstract: In quantum mechanics textbook, the spherical coordinate forms of both L^2 and L^x are obtained generally by using the Cartesian coordinates, however, the variable substitution calculation is complex. In this paper, the spherical coordinates on the orthogonal basis of coordinate are regarded to variables vectors, and differential nature of the spherical coordinates is used. The derivation for angular momentum operators L^2 and L^x in quantum mechanics is predigested.

Key words: spherical coordinates, angular momentum operator, momentum operator, simplified derivation