Angular momentum and the rotation group

S. Rajasekar, R. Velusamy

A particle moving along a straight-line has a linear momentum mv. A revolving particle has angular momentum due to its mass and angular velocity. Let us imagine the electron as a small ball, revolving about some axis. It possesses angular momentum. Precisely, the angular momentum vector is a vector pointing along the axis of rotation with magnitude proportional to the speed of rotation. In classical mechanics the symmetry of a physical system leads to conservation laws. If the space is isotropic, it possesses rotational symmetry. The number of elements in a group is called its order. A group with finite number of elements is called a finite group whereas an infinite group contains infinite number of elements. An infinite group may further be either discrete or continuous. In fact, it is impossible to tell whether an electron is spinning. The word spin is a convenient way of representing the intrinsic angular momentum of a particle.

D. Dubbers, H.‐J. Stöckmann

Bipin R. Desai

Ahmad Aqwa Rosli, Nurisya Mohd Shah

The purpose of this work is to investigate the mathematical structure of finite quantum angular momentum in a specific direction L3 which can be constructed from the representation of the U(1) group. The angular momentum eigenstate is invariant under Abelian rotation symmetry. The character group of U(1) is constructed to show that there exists an additive unitary operator for the angular momentum eigenstate, and the rotation eigenstate is invariant under it. The Weyl relation is proved by showing that the angle and angular momentum L3 are the canonical conjugate pair of observables.

‎Louis Marchildon

Jerome K. Percus, A. Rotenberg

By an appropriate rotational procedure, a projection operator can be constructed to give exact eigenfunctions of angular momentum. Applications to cases involving spin and orbital angular momentum are given and, in particular, all spin multiplets of the alternant molecular structure are obtained. The connection with the group theoretical approach is discussed.