kvantnummer

Kvantnummer (quantum number) is a label assigned to quantum states in quantum mechanics, arising from the quantization of observables such as energy and angular momentum. They are used to describe properties of particles like electrons in atoms or molecules and help specify allowed states and transitions.

In atoms, the common set includes the principal quantum number n (positive integer), the orbital angular momentum quantum number l (0 to n−1), the magnetic quantum number m_l (−l to +l), and the spin quantum number m_s (−1/2 or +1/2). These numbers define the electron's state and contribute to energy levels and degeneracy, particularly in hydrogen-like systems.

When spin-orbit coupling is included, the total angular momentum quantum number j (from |l−s| to l+s) and its projection m_j are used, sometimes along with parity. Additional quantum numbers may be invoked in more complex systems (nuclear spin, isospin, etc.). In molecules, quantum numbers describe vibrational and rotational levels (e.g., vibrational v, rotational J and K). Electronic, vibrational, and rotational quantum numbers combine to label molecular states.

Practically, kvantnummer label energy levels, determine selection rules for transitions, and influence spectral lines and degeneracies. They provide a compact way to describe the structure of quantum systems and the possible transitions between states.

The concept emerged from early quantum theory and the solution of the Schrödinger equation for atoms, building on Bohr’s model and Planck's constant. It remains a fundamental tool across atomic, molecular, and condensed-mmatter physics.