COORDINATE-FREE ROTATION OPERATOR

The use of a coordinate-free rotation operator is suggested for the teaching of rotations in Euclidean three space because of its twofold didactic advantage. On the one hand, the only ingredients of the simply structured rotation operator are axis and angle of rotation, in terms of which the student conceives an actual physical rotation. Thus, he is able to write down immediately the correct rotation operator or sequence of rotation operators. Scalar multiplication by the members of a particular set of basis vectors subsequently produces a particular representation in an unambiguous way. On the other hand, the use of the rotation operator as distinct from its various representations stresses the existence of vectors and operators as physical entities independent of an observer’s frame and thus prepares the student at an elementary level for a similar language in modern quantum theory. The potentialities of the coordinate-free rotation operator approach are illustrated by a number of examples. © 1979, American Association of Physics Teachers. All rights reserved.