Kvantnumbrid

Kvantnumbrid, or quantum numbers, are a set of values that label the quantum states of a system and determine the allowed values of observables such as energy, angular momentum, and spin. They arise from solving the quantum equations for a system and correspond to eigenvalues of commuting operators.

In atomic physics, the most common quantum numbers describe an electron in an atom: the principal quantum number n, the orbital angular momentum quantum number l, the magnetic quantum number m_l, and the spin quantum number m_s. n is a positive integer (1, 2, 3, ...); l ranges from 0 to n−1; m_l runs from −l to +l; and m_s is ±1/2 for electrons. A related radial quantum number n_r can be defined as n_r = n − l − 1.

When spin–orbit coupling is considered, additional numbers appear: the total angular momentum j (j = l ± s for s = 1/2) and its projection m_j. Parity and other symmetries can also label states. In hydrogen-like atoms, energy depends primarily on n, while in multi-electron atoms fine structure depends on l and j.

Quantum numbers also generalize to molecules and solids, where rotational and vibrational numbers label molecular states, or crystal momentum k labels Bloch states in solids. Quantum numbers are eigenvalues of commuting operators and provide a compact way to categorize and predict spectra, selection rules, and transition probabilities.