Rotations of Angular Momentum Operators

Gordon Baym

The orbital angular momentum of a particle in quantum mechanics is defined exactly as in classical mechanics. Before developing any properties of the angular momentum operators, students must know the commutation relations they satisfy with themselves, with the momentum operator, and with the position operator. The angular momentum operator is very closely related to rotations of the system. Students should compare the ability of the angular momentum operator to generate infinitesimal rotations, with the corresponding property of the linear momentum p. The chapter provides the theory of the orbital angular momentum sufficiently to study the problem of a particle in a central potential.

Vishnu S. Mathur, Surendra Singh

The invariance of the Hamiltonian of a physical system under spatial rotation, together with the connection between the rotation operator Rˆn(θ) and the angular momentum operator Jˆ ≡ (Jˆx, Jˆy, Jˆz), leads to the principle of conservation of angular momentum [Chapter 6, Sec. 6.3] and to the status of total angular momentum as a constant of motion. This makes angular momentum a very important quantity in quantum mechanics.

Nandita Rudra

The angular momentum operator is closely related to rotation in space. The quantum mechanical definition of angular momentum differs from the classical definition r × p of angular momentum. This expression is not sufficiently general as it cannot yield spin angular momentum which does not have a classical counterpart without having any coordinate representation.

Giampiero V. M. Esposito, Giuseppe Marmo, George Sudarshan