Jtotal

Jtotal, often written as Jtot or simply J in context, denotes the total angular momentum of a quantum system. In quantum mechanics, angular momentum is described by the vector operator J, which can be decomposed into orbital and spin parts. The total angular momentum operator satisfies J^2 |j m_j> = ħ^2 j(j+1) |j m_j> and J_z |j m_j> = ħ m_j |j m_j>, where j is the total angular momentum quantum number (which can be integer or half-integer) and m_j is its projection along a chosen axis.

In many-body systems, Jtotal arises from coupling the angular momenta of subsystems, such as orbital angular momentum L and spin S, via J = L + S. Different coupling schemes exist, notably LS (Russell-Saunders) coupling, where L and S are coupled first to form J, and jj coupling, where individual orbital and spin angular momenta couple stepwise to the total J. Clebsch–Gordan coefficients describe how product states combine into total J states.

Jtotal plays a central role in atomic and nuclear physics. It determines the fine structure of atomic energy levels, governs selection rules for radiative transitions, and influences Zeeman splittings in magnetic fields. The Landé g-factor relates J, L, and S to magnetic response. In broader contexts, Jtotal may refer to the total angular momentum of a nucleus or particle system, or appear in formulas involving total angular momentum in scattering and reaction theory. Context usually clarifies whether J denotes total angular momentum or another quantity sometimes labeled Jtot.