kvantetalene

The kvantetalene are a set of discrete quantum numbers that label the quantum states of particles in quantum systems, most notably electrons in atoms. They arise from solving the quantum mechanical equations and reflect conserved quantities such as energy, angular momentum, and spin.

Common quantum numbers in atomic physics: principal n (positive integer), orbital angular momentum l (0 to n-1), magnetic m_l (-l to l), spin s (1/2 for electrons), spin projection m_s (-1/2, +1/2). When coupling orbital and spin, total angular momentum j and its projection m_j arise. In multi-electron atoms, LS or jj coupling labels.

The mathematical basis: In a central Coulomb potential, separation of variables yields radial part R_{n,l}(r) and angular part Y_l^m, giving eigenvalues for energy depending on n in hydrogen-like atoms; spin is described by Pauli matrices; the Pauli exclusion principle states that no two electrons share identical set of numbers.

Usage and implications: Determine electron configurations, spectral lines, and chemical properties. In spectroscopy, transitions involve changes in quantum numbers subject to conservation laws. In more complex atoms, additional quantum numbers describe fine structure, hyperfine structure, and electron correlation.

Etymology/Notes: The term comes from quantum theory; "kvantetalene" in Norwegian or equivalent translation.